Mathematical geometric reasoning solving method and system for multi-modal large language model

Abstract

The invention discloses a mathematical geometric reasoning solving method and system of a multi-modal large language model, and relates to the technical field of artificial intelligence and education, and the method comprises the steps: receiving a user question containing geometric figures and text descriptions, and carrying out the multi-modal feature coding and fusion of the user question through the multi-modal large language model, generating a multi-modal problem representation; inputting the multi-modal problem representation into a reverse thinking reasoning template, and guiding a multi-modal large language model to generate a structured reasoning process; inputting the structured reasoning process into a program auxiliary execution template, and guiding the multi-modal large language model to convert the structured reasoning process into an executable code block; and executing the executable code block through an external code interpreter, and outputting a numerical result obtained by execution as an answer to the user question. According to the method, the accuracy and reliability of the multi-modal large language model on mathematical geometry problems can be remarkably improved without fine adjustment of the model, and the interpretability of the solving process is enhanced.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and education technology, and in particular to a method and system for solving mathematical geometric reasoning problems of multimodal large language models. Background Technology

[0002] With the widespread application of multimodal large language models (i.e. models that process both image and text inputs simultaneously) in tasks such as visual question answering and conventional mathematical problems, researchers are gradually trying to apply them to solving mathematical geometry problems.

[0003] However, significant challenges remain when faced with typical mathematical geometry problems—that is, problems containing diagrams (such as constructed diagrams or labeled diagrams), textual descriptions (problem stems and mathematical / geometric conditions), and mathematical / geometric operations (such as angle calculations, length calculations, area calculations, and mathematical / geometric relationships). 1. The model must have knowledge of mathematical geometry (such as the properties of parallel lines, similar triangles, the properties of tangents to circles, and the construction of polygons) to understand the relationships between figures.

[0004] 2. The model must perform precise arithmetic / algebraic operations (e.g., solving equations, calculating ratios, substituting length expressions and area formulas), as direct output from the language model is prone to errors.

[0005] 3. While existing hinting engineering techniques (such as Chain-of-Thought and Program-Aided Language) demonstrate strong capabilities in general mathematical reasoning tasks, they still have significant limitations in mathematical geometry problem scenarios. First, while Chain-of-Thought hints can guide the model to think step-by-step and generate reasoning chains, their broad applicability makes it difficult to accurately model the structural relationships, theorems, and spatial relationships within mathematical geometric figures, often overlooking specific mathematical geometric structures. Second, although Program-Aided Language hints can guide the model to generate executable code, which can then be computed through an external interpreter, thus improving the accuracy of numerical calculations, they lack a hinting structure specifically designed for mathematical geometry problems, making it difficult to fully reflect the reverse thinking characteristic of mathematical geometry (i.e., tracing back mathematical geometric relationships from the problem objective). Since neither of these methods effectively integrates knowledge and reasoning frameworks from the field of mathematical geometry, their performance in solving mathematical geometry problems still fails to meet the requirements of high precision and high reliability.

[0006] Therefore, it is necessary to propose a new prompting method and system specifically to address the combined challenge of "mathematical geometry knowledge reasoning + precise arithmetic execution" in mathematical geometry problems. Summary of the Invention

[0007] To address the issue of the separation between textual and graphical information in mathematical geometry problems, which makes it difficult for models to deeply understand and collaboratively utilize the complementary information contained in both, this paper proposes a method and system for mathematical geometry reasoning and solving using a multimodal large language model. By constructing prompt templates that coordinate reasoning and execution, the method effectively guides the multimodal large language model to simulate human problem-solving thinking, thereby improving the accuracy and reliability of solving mathematical geometry problems.

[0008] On the one hand, to achieve the above objectives, this invention provides a method for solving mathematical and geometric reasoning problems in multimodal large language models, including: The system receives user questions containing geometric figures and text descriptions, and uses a multimodal large language model to encode and fuse the user questions to generate a multimodal question representation. The multimodal problem representation is input into the reverse thinking reasoning template to guide the multimodal large language model to generate a structured reasoning process, wherein the structured reasoning process includes: at least one geometric domain knowledge required to solve the problem, data related to the geometric domain knowledge extracted from the user problem, and arithmetic calculation requirements derived based on the geometric domain knowledge and the data; The structured reasoning process is input into the program-assisted execution template, which guides the multimodal large language model to transform the structured reasoning process into an executable code block. The program variables in the executable code block have a semantic mapping relationship with the mathematical symbols in the structured reasoning process. The executable code block is executed by an external code interpreter, and the resulting numerical value is output as the answer to the user's question.

[0009] Preferably, the multimodal feature encoding and fusion includes: The geometric shape is encoded using an image encoder to obtain an image feature vector; The text description and problem-solving objective are encoded using a text encoder to obtain a text feature vector; The image feature vector and the text feature vector are projected into the same latent space and fused to generate the multimodal problem representation.

[0010] Preferably, the reverse thinking reasoning template is constructed using a reverse thinking method to guide the large language model in reasoning, including: First, identify and anchor the core geometric theorems or properties that are directly related to the solution objective; Secondly, based on the core geometric theorems or properties, known conditional data are extracted from the multimodal problem representation; Finally, the core geometric theorems and the known conditional data are integrated to form a specific arithmetic process description.

[0011] Preferably, the reverse thinking is integrated into the multimodal large language model through a few-sample prompting method.

[0012] Preferably, the program-aided execution template is used to standardize code generation, including: Based on the arithmetic computation requirements defined in the structured reasoning process, an execution function framework with a unified name is defined; Within the execution function framework, a deterministic naming rule is established from natural language mathematical symbols in the structured reasoning process to program variables; Generate code text that conforms to the syntax of the target programming language, including complete variable assignments, evaluation expressions, and result return statements.

[0013] Preferably, the executable code block generated by the program-assisted execution template is Python code.

[0014] On the other hand, to achieve the above objectives, the present invention also provides a mathematical and geometric reasoning solution system for multimodal large language models, comprising: The multimodal understanding and encoding module is used to receive and jointly encode the user input of geometric figures and text descriptions of the problem, and output a multimodal problem representation; The reverse reasoning guidance module, which has an embedded reverse thinking reasoning template, is used to receive the multimodal problem representation and guide the multimodal large language model to output a structured reasoning process. The programmatic execution guidance module, which has an embedded program-assisted execution template, is used to receive the structured reasoning process and guide the multimodal large language model to output executable code blocks. The code execution and output module is used to call an external interpreter to run the executable code block and output the final answer.

[0015] Preferably, the reverse reasoning guidance module and the programmed execution guidance module work together in series, wherein the output of the reverse reasoning guidance module serves as the input of the programmed execution guidance module.

[0016] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the mathematical and geometric reasoning solution method for a multimodal large language model.

[0017] The present invention also provides a computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the mathematical and geometric reasoning solution method for the multimodal large language model.

[0018] Compared with the prior art, the present invention has the following advantages and technical effects: (1) Significantly improves the accuracy and reliability of problem solving: Compared with traditional prompting methods (such as Chain-of-Thought and Program-Aided Language), this invention effectively alleviates the two core problems of inaccurate reasoning and inaccurate calculation in solving geometric problems in multimodal large language models through the dual-stage collaborative design of "reverse thinking reasoning template" and "program-aided execution template". (2) Realize domain knowledge-driven structured reasoning: This invention proposes for the first time to use the reverse thinking method to construct a reverse thinking reasoning template, guiding the model to start from the geometric theorems and properties most relevant to the problem, and gradually deduce to the specific arithmetic requirements, forming a reasoning chain; (3) No model fine-tuning required, plug and play, strong applicability: This invention is based on prompting engineering, which does not require parameter fine-tuning or additional training of multimodal large language models, does not rely on a large amount of labeled data, and saves computing resources and time costs. This method is applicable to a variety of open source and closed source multimodal large language models (such as GPT, Gemini, Qwen-VL, etc.), and has good model universality and scenario scalability. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a mathematical and geometric reasoning solution method for a multimodal large language model according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the reverse reasoning guidance module according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the programmatic execution boot module according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the code execution and output module according to an embodiment of the present invention; Figure 5 This is an example diagram of executable mathematical geometry problem-solving code according to an embodiment of the present invention; Figure 6 This is a schematic diagram of a prompt template according to an embodiment of the present invention. Detailed Implementation

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0022] This embodiment proposes a mathematical and geometric reasoning solution method for multimodal large language models, such as... Figure 1 ,include: The system receives user questions containing geometric figures and text descriptions, and uses a multimodal large language model to encode and fuse the user questions to generate a multimodal question representation. The multimodal problem representation is input into the reverse thinking reasoning template to guide the multimodal large language model to generate a structured reasoning process, wherein the structured reasoning process includes: at least one geometric domain knowledge required to solve the problem, data related to the geometric domain knowledge extracted from the user problem, and arithmetic calculation requirements derived based on the geometric domain knowledge and the data; The structured reasoning process is input into the program-assisted execution template, which guides the multimodal large language model to transform the structured reasoning process into an executable code block. The program variables in the executable code block have a semantic mapping relationship with the mathematical symbols in the structured reasoning process. The executable code block is executed by an external code interpreter, and the resulting numerical value is output as the answer to the user's question.

[0023] Further, the multimodal feature encoding and fusion are performed, including: The geometric shape is encoded using an image encoder to obtain an image feature vector; The text description and problem-solving objective are encoded using a text encoder to obtain a text feature vector; The image feature vector and the text feature vector are projected into the same latent space and fused to generate the multimodal problem representation.

[0024] Specifically, the system receives mathematical geometry problems input by users, which include text descriptions and mathematical geometry figures. The visual and language encoders of a multimodal large language model are used to jointly encode the text descriptions and mathematical geometry figures to form a fused multimodal problem representation.

[0025] In other words, the input for a geometry problem includes not only the textual description of the problem statement, but also geometrically constructed diagrams (such as planar diagrams, labeled diagrams, auxiliary line diagrams, etc.) and the solution objective. To facilitate unified understanding, processing, and reasoning by the model, the information from each modality (text + image + target structure) must be represented in a unified manner.

[0026] Let the geometric problem be q = (I, T, G); Where I represents the geometric construction image, reflecting the graphic elements (points, lines, angles, circles, auxiliary lines, etc.) and their spatial / topological relationships; T represents the textual description of the problem stem, including known conditions (such as "AB∥CD", "∠A=60"), textual explanations in the figure, and solution hints; G represents the solution objective, such as "find ∠BCD" or "find the area of ​​triangle ABC".

[0027] To integrate different modal inputs into a unified modeling framework, this embodiment uses modal encoders to uniformly convert (I,T,G) into a processable numerical representation. Each modality is mapped to a corresponding feature vector. Let: Vimg=Eimg(I), Vtxt=Etxt(T), Vtgt=Etgt(G); Where Eimg(·) is an image encoder that maps the geometrically constructed image I to the vector Vimg; Etxt(·) and Etgt(·) are text encoders for the question stem and the solution target, respectively, mapping the question stem and the solution target G to the vectors Vtxt and Vtgt.

[0028] Project the vectors Vimg, Vtxt, and Vtgt onto a unified dimensional space: eimg=Pimg(Vimg), etxt=Ptxt(Vtxt), etgt=Ptgt(Vtgt); Where eimg is the image projection feature vector, Pimg is the image projection mapping function, etxt is the text projection feature vector, Ptxt is the text projection mapping function, etgt is the target projection feature vector, and Ptgt is the target projection mapping function; P is a mapping function, in the following form: Pi = Wivi + bi; In the formula, W∈Rd d is the projection matrix, b∈Rd is the bias vector, Wi is the projection weight matrix of the i-th mode, vi is the feature vector of the i-th mode after being encoded by the encoder, bi is the bias vector of the corresponding projection transformation, and Pi is the projection function of the corresponding mode.

[0029] Furthermore, the reverse thinking reasoning template is constructed using reverse thinking methods to guide the large language model in reasoning, including: First, identify and anchor the core geometric theorems or properties that are directly related to the solution objective; Secondly, based on the core geometric theorems or properties, known conditional data are extracted from the multimodal problem representation; Finally, the core geometric theorems and the known conditional data are integrated to form a specific arithmetic process description.

[0030] Specifically, the reverse thinking reasoning template represents multimodal problems and, together with a pre-set reasoning template, generates a structured reasoning process, enabling domain knowledge anchoring and multimodal data association and extraction.

[0031] The reverse thinking reasoning template is constructed using reverse thinking methods to guide the model to reason according to the following logic: Domain knowledge identification: Identify and list one or more geometric theorems, formulas, or properties required to solve the problem; Available data extraction: Identify symbols and their specific values ​​related to domain knowledge from the text and graphics of the problem; The arithmetic requirements are clearly defined: by integrating domain knowledge and available data, the specific arithmetic calculation process required to solve the problem is clearly described.

[0032] The above process is represented as follows: Let a geometry problem be represented by a triple, where I is the geometric construction diagram, T is the textual description of the problem statement, and G is the solution objective: q=(I,T,G); Multimodal information encoding and fusion: Vfusion=Fusion(Eimg(I),Etxt(T),Etgt(G)); Fusion(·) is a cross-modal feature fusion function.

[0033] Domain knowledge anchoring and data association extraction: K = KnowledgeAnchor(Vfusion); D = DataExtract(Vfusion, K); Where K={K1,K2,....,Km} is the set of identified geometric theorems, formulas or properties; Vfusion is the output of the cross-modal feature fusion machine; D is the set of symbol-numerical pairs extracted from the text and image information and is associated with knowledge K.

[0034] The final structured reasoning process is as follows: R=(K,D,C); Where C is the calculation process based on the identified set of geometric theorems, formulas or properties and the set of symbol-numerical pairs extracted from graphic information, and R is the geometric relationship derivation chain.

[0035] Furthermore, the reverse thinking is integrated into the multimodal large language model through a few-sample prompting method.

[0036] Furthermore, the program-aided execution template is used to standardize code generation, including: Based on the arithmetic computation requirements defined in the structured reasoning process, an execution function framework with a unified name is defined; Within the execution function framework, a deterministic naming rule is established from natural language mathematical symbols in the structured reasoning process to program variables; Generate code text that conforms to the syntax of the target programming language, including complete variable assignments, evaluation expressions, and result return statements.

[0037] Specifically, this step is crucial for ensuring the accuracy of the results, realizing the transformation from "thinking" to "action." It combines the generated rigorous reasoning process with a program-assisted execution template to produce an executable code block with standardized variable naming and perfectly matched logic. Figure 4 It can be viewed as a complete overall prompt template containing reasoning and execution parts. The program-assisted execution template is the code execution part of the overall prompt template, and its structure is similar to... Figure 4 The code execution part is the same.

[0038] Program-assisted execution templates are used as prompts to guide multimodal large language models: Based on the explicit arithmetic requirements during the reasoning process, a unified execution framework for computational reduction is first established (by defining the `def solution()` function in the code block). This step provides a well-encapsulated container for all subsequent computational logic, one that can be recognized and invoked by the standard interpreter. Within the initialized framework, establish and implement a semantic mapping from mathematical symbols in the reasoning process to program variables. It is required that every variable name in the code strictly corresponds to and is semantically transparent with the mathematical symbols in the reasoning process (e.g., angle_A corresponds to ∠A). Generate complete, computer-executable formally evaluated expressions without any unassigned variables; Answer=Mexec(Mcode(Mmodel(Mreason(Mprompt{(qi,ri,bi)},q)))); Where qi is the i-th example question, ri is the i-th example reasoning process, bi is the i-th executable code block, Mprompt is the general hint template, Mmodel is the model interface, Mreason is the reverse reasoning template, Mcode is the code generation template, and Mexec is the code execution template.

[0039] The program-assisted execution template uses uniform code block naming (e.g., def solution():) based on the explicit arithmetic requirements in the reasoning process; adopts meaningful variable naming to ensure that variables in the code strictly correspond to symbols in the reasoning process (e.g., angle_A corresponds to ∠A); and generates complete Python code without any unassigned variables.

[0040] This embodiment also provides a mathematical geometric reasoning solution system for a multimodal large language model, used to implement a mathematical geometric reasoning solution method for a multimodal large language model, including: The multimodal understanding and encoding module is used to receive and jointly encode the user input of geometric figures and text descriptions of the problem, and output a multimodal problem representation; The reverse reasoning guidance module, which has an embedded reverse thinking reasoning template, is used to receive the multimodal problem representation and guide the multimodal large language model to output a structured reasoning process. The programmatic execution guidance module, which embeds a program-assisted execution template, is used to receive the structured reasoning process and guide the multimodal large language model to output executable code blocks, such as... Figure 3 ; The code execution and output module is used to call an external interpreter to run the executable code block and output the final answer.

[0041] Furthermore, the reverse reasoning guidance module and the programmed execution guidance module work together in series, wherein the output of the reverse reasoning guidance module serves as the input of the programmed execution guidance module, such as... Figure 2 .

[0042] Specifically, the processing procedures between the modules can be represented by the following formulas / relationships: Model interface: ejoint=Mmodel(P,q); Reverse reasoning guidance module: rtest=Mreason(ejoint); Programmatic execution of the bootstrap module: btest = Mcode(rtest, ejoint); Code execution and output module: A = Mexec(btest); Where ejoint represents the joint feature representation vector of the multimodal geometric problem, P is the mapping function, q is the geometric problem, rtest is the geometric reasoning process representation, Mreason is the reverse thinking reasoning template, btest is the executable logical expression generated by rtest, Mcode is the code generation template, Mexec is the code execution template, and A is the final answer obtained after btest is executed.

[0043] Furthermore, the executable code block generated by the prompt template is submitted to the Python interpreter for execution, and the numerical result calculated by the interpreter is output as the final answer to the geometry problem.

[0044] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the mathematical and geometric reasoning solution method for a multimodal large language model.

[0045] A computer-readable storage medium storing computer instructions that, when executed by a processor, implement a mathematical and geometric reasoning solution method for a multimodal large language model.

[0046] To more clearly illustrate the technical solution of the present invention, specific embodiments are provided below for description: The following detailed description of this technical solution uses a more complex embodiment as an example. Figure 5 , Figure 6 Let's take solving a mathematical geometry problem as an example: S1. Problem Input and Multimodal Information Encoding: The user entered the question: "As shown in the figure, in △ABC, ∠A=80°, ∠B=60°, DE∥BC, find the measure of ∠CED." (Mathematical geometry and...) Figure 2 (The issues are consistent) The system receives the question, which includes a textual description and a mathematical geometric image of a triangle.

[0047] The multimodal large language model performs joint encoding of text and image information, and understands that there is a triangle ABC and an auxiliary line DE in the image, where DE∥BC, point E is located on AC, and point D is located on AB.

[0048] S2. Generation of rigorous reasoning process: Domain knowledge identification: 1. Parallel lines corresponding angle theorem: If DE∥BC, then ∠CED=180°−∠C (property of alternate interior angles or corresponding angles); 2. Triangle Angle Sum Theorem: In △ABC, ∠A + ∠B + ∠C = 180°, so ∠C = 180° - ∠A - ∠B.

[0049] 3. Properties of the radius of a circle: The radii of semicircles are equal, OB=OC=OE=3cm.

[0050] 4. Angle substitution relationship: Substituting the expression of ∠C into ∠CED=180°−∠C, we can get ∠CED=180°−(180°−∠A−∠B)=∠A+∠B.

[0051] Available data extraction: 1. From the question, we can directly obtain: ∠A = 80°, ∠B = 60°; 2. It can be derived that ∠C = 180° − 80° − 60° = 40°.

[0052] The arithmetic requirements are clear: 1. Substituting into the parallel line property formula: ∠CED = 180° − ∠C = 180° − 40° = 140°.

[0053] By proving that △ABO∽△EDO, we can establish the proportional relationship: AB / ED=AO / EO.

[0054] 2. Verification: ∠CED=∠A+∠B=80°+60°=140°, which is consistent with the above formula.

[0055] S3. Executable code block generation: Guided by the program-assisted execution template, the model generates, based on the above reasoning process, the following: Figure 5 The Python code block shown.

[0056] S4. Answer Acquisition and Output: The system calls the Python interpreter to execute the `solution()` function. After performing the calculation, the interpreter returns the numerical result of `angle_CED`. The system outputs this result to the user. Simultaneously, the system can optionally provide the user with the complete inference text generated by S2 and the source code generated by S3 for review and learning.

[0057] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for solving mathematical and geometric reasoning problems in a multimodal large language model, characterized in that, include: The system receives user questions containing geometric figures and text descriptions, and uses a multimodal large language model to encode and fuse the user questions to generate a multimodal question representation. The multimodal problem representation is input into the reverse thinking reasoning template to guide the multimodal large language model to generate a structured reasoning process, wherein the structured reasoning process includes: at least one geometric domain knowledge required to solve the problem, data related to the geometric domain knowledge extracted from the user problem, and arithmetic calculation requirements derived based on the geometric domain knowledge and the data; The structured reasoning process is input into the program-assisted execution template, which guides the multimodal large language model to transform the structured reasoning process into an executable code block. The program variables in the executable code block have a semantic mapping relationship with the mathematical symbols in the structured reasoning process. The executable code block is executed by an external code interpreter, and the resulting numerical value is output as the answer to the user's question.

2. The mathematical and geometric reasoning solution method for multimodal large language models according to claim 1, characterized in that, The multimodal feature encoding and fusion includes: The geometric shape is encoded using an image encoder to obtain an image feature vector; The text description and problem-solving objective are encoded using a text encoder to obtain a text feature vector; The image feature vector and the text feature vector are projected into the same latent space and fused to generate the multimodal problem representation.

3. The mathematical and geometric reasoning solution method for multimodal large language models according to claim 1, characterized in that, The reverse thinking reasoning template is constructed using reverse thinking methods and is used to guide the large language model in reasoning, including: First, identify and anchor the core geometric theorems or properties that are directly related to the solution objective; Secondly, based on the core geometric theorems or properties, known conditional data are extracted from the multimodal problem representation; Finally, the core geometric theorems and the known conditional data are integrated to form a specific arithmetic process description.

4. The mathematical and geometric reasoning solution method for multimodal large language models according to claim 3, characterized in that, The reverse thinking is integrated into the multimodal large language model through a few-sample prompting method.

5. The mathematical and geometric reasoning solution method for multimodal large language models according to claim 1, characterized in that, The program-aided execution template is used to standardize code generation, including: Based on the arithmetic computation requirements defined in the structured reasoning process, an execution function framework with a unified name is defined; Within the execution function framework, a deterministic naming rule is established from natural language mathematical symbols in the structured reasoning process to program variables; Generate code text that conforms to the syntax of the target programming language, including complete variable assignments, evaluation expressions, and result return statements.

6. The mathematical and geometric reasoning solution method for multimodal large language models according to claim 5, characterized in that, The executable code block generated by the program-assisted execution template is Python code.

7. A mathematical geometric reasoning system for solving a multimodal large language model, used to implement the mathematical geometric reasoning solution method for the multimodal large language model according to any one of claims 1-6, characterized in that, include: The multimodal understanding and encoding module is used to receive and jointly encode the user input of geometric figures and text descriptions of the problem, and output a multimodal problem representation; The reverse reasoning guidance module, which has an embedded reverse thinking reasoning template, is used to receive the multimodal problem representation and guide the multimodal large language model to output a structured reasoning process. The programmatic execution guidance module, which has an embedded program-assisted execution template, is used to receive the structured reasoning process and guide the multimodal large language model to output executable code blocks. The code execution and output module is used to call an external interpreter to run the executable code block and output the final answer.

8. The mathematical and geometric reasoning solution system for multimodal large language models according to claim 7, characterized in that, The reverse reasoning guidance module and the programmed execution guidance module work together in series, wherein the output of the reverse reasoning guidance module serves as the input of the programmed execution guidance module.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described in any one of claims 1-6.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, they implement the method as described in any one of claims 1-6.

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