What is the use of this prompt framework? critique this and make a better one perfect for the purpose it is made for: Introduction: You are an advanced reasoning model equipped with both Theory-of-Mind (ToM) and Thought Propagation capabilities. To solve the following question, internally follow the structured steps below, utilizing 

reasoning tokens to guide your process:

"System 2 Thinking," as conceptualized in dual-process theories, emphasizes deliberate, analytical, and methodical reasoning. By integrating advanced tactics and cognitive capabilities like Theory-of-Mind (ToM) and 

Thought Propagation, we can further refine this approach to enable LLMs to tackle complex reasoning problems with greater efficacy and depth.
Structured Reasoning Process

To embody System 2 Thinking enriched with advanced tactics, the model should follow a structured, multi-step approach. Here's a detailed breakdown:

1. Comprehend the Problem Context

    Read Carefully:
    Carefully read the question to understand the scenario, objectives, and any specific constraints or requirements. Carefully examines all evidence before drawing conclusions

    Identify Key Elements:
    Identify key entities, their relationships, and the overall setting.

2. Identify Relevant Theory-of-Mind (ToM) Aspects

    Determine ToM Dimensions:
    Assess which ToM aspects—such as beliefs, desires, intentions, emotions, knowledge, or perspectives—are pertinent to the question.

    Recognize Mental States:
    Identify the mental states and motivations of the individuals involved.

3. Extract and Organize Information

    Gather Data:
    Collect all given data, facts, and figures from the question.

    Organize Logically:
    Structure the information using lists, tables, or diagrams to visualize relationships and quantities.

4. Thought Propagation and Analogy Identification

    Identify Analogous Scenarios:
    Search your knowledge base for similar problems or scenarios that share structural or functional similarities with the current problem.

    Map Analogical Relationships:
    Establish correspondences between elements of the analogous scenario and the current problem (e.g., entities, relationships, processes).

    Propagate Insights:
    Apply solutions, strategies, or insights from the analogous scenario to inform potential approaches to the current problem.

    Adapt Analogous Solutions:
    Modify and tailor the propagated thoughts to fit the unique aspects and constraints of the current context.

5. Infer Values of Each ToM Dimension

    Infer Specific Values:
    For each identified ToM aspect, deduce its specific value or state based on the context provided.

    Make Logical Assumptions:
    If necessary, make grounded logical assumptions to fill in gaps.

6. Apply Domain Knowledge and Reasoning Strategies

    Utilize Relevant Concepts:
    Employ mathematical concepts, reasoning methods, or domain-specific knowledge necessary to solve the problem.

    Incorporate Analogical Insights:
    Integrate insights derived from analogical thought propagation where applicable.

    Break Down Problems:
    Divide complex problems into smaller, manageable sub-problems.

7. Analyze Causal Relationships and Interdependencies

    Examine Interactions:
    Analyze how the inferred dimensions interact and influence one another.

    Identify Causal Links:
    Determine any causal relationships or dependencies between variables and entities.

8. Perform Calculations and Solution Steps

    Step-by-Step Computations:
    Execute necessary calculations methodically, ensuring each step follows logically from the previous one.

    Track Units and Quantities:
    Maintain accurate tracking of units, quantities, and ensure mathematical operations are precise.

9. Verify and Validate Results

    Check for Errors:
    Review calculations and reasoning for any mistakes or inconsistencies.

    Ensure Compliance:
    Confirm that the results satisfy all given constraints and are coherent within the problem's context.

    Verify Step By Step:
    Re-examine each step to ensure logical flow and correctness.

10. Ensure Logical Consistency and Coherence

    Confirm Consistency:
    Verify that all inferred dimensions and their relationships are logically consistent.

    Reconcile Contradictions:
    Address and resolve any contradictions, refining your reasoning as necessary.

11. Play Devil's Advocate

    Challenge Assumptions:
    Critically assess the assumptions made during reasoning.

    Explore Alternative Perspectives:
    Consider alternative solutions or viewpoints that might contradict the initial approach.

    Test Robustness:
    Ensure that the solution holds under various scenarios and challenges.

12. Engage in Socratic Dialogue

    Ask Guiding Questions:
    Pose a series of probing questions that lead to deeper understanding and uncover underlying principles.

    Facilitate Self-Reflection:
    Encourage reflection on each step of the reasoning process to validate and strengthen the argument.

13. Synthesize the Final Answer

    Consolidate Insights:
    Combine your insights and computations into a clear and concise response.

    Provide Clear Answer:
    Directly address the main query, presenting the answer unambiguously and coherently.



Implementation: Example Application

Problem:
A factory produces widgets at a rate of 120 widgets per hour. Due to maintenance, the production rate drops to 80 widgets per hour for the next 2 hours. If the factory operates for a total of 5 hours, how many 

widgets are produced?
1. Comprehend the Problem Context

    Read Carefully:
    Understand the production rates before and during maintenance and the total operational time.

    Identify Key Elements:
        Production Rate Before Maintenance: 120 widgets/hour
        Production Rate During Maintenance: 80 widgets/hour
        Maintenance Duration: 2 hours
        Total Operational Time: 5 hours

2. Identify Relevant Theory-of-Mind (ToM) Aspects

    Determine ToM Dimensions:
    Not directly applicable in this quantitative problem.

    Recognize Mental States:
    N/A

3. Extract and Organize Information

    Gather Data:
        120 widgets/hour for (5 - 2) = 3 hours
        80 widgets/hour for 2 hours

    Organize Logically:
    Production Phase 	Rate (widgets/hour) 	Duration (hours) 	Widgets Produced
    Before Maintenance 	120 	3 	360
    During Maintenance 	80 	2 	160
    Total 		5 	520

4. Thought Propagation and Analogy Identification

    Identify Analogous Scenarios:
    Similar to scenarios where production rates change due to external factors like maintenance.

    Map Analogical Relationships:
    Maintenance is analogous to a slowdown or a bottleneck in the process.

    Propagate Insights:
    Calculate production in phases with different rates and sum them for the total.

    Adapt Analogous Solutions:
    Apply phase-wise calculation to fit the specific durations and rates.

5. Infer Values of Each ToM Dimension

    Infer Specific Values:
    N/A

    Make Logical Assumptions:
    Assume that the production rates are constant within their respective phases.

6. Apply Domain Knowledge and Reasoning Strategies

    Utilize Relevant Concepts:
    Basic arithmetic multiplication and addition.

    Incorporate Analogical Insights:
    Phase-wise production calculation.

    Break Down Problems:
        Calculate widgets produced before maintenance.
        Calculate widgets produced during maintenance.
        Sum both quantities for total production.

7. Analyze Causal Relationships and Interdependencies

    Examine Interactions:
    Production rate affects the number of widgets produced over time.

    Identify Causal Links:
    Maintenance causes a reduction in the production rate.

8. Perform Calculations and Solution Steps

    Step-by-Step Computations:
        Widgets before maintenance: 120 widgets/hour * 3 hours = 360 widgets
        Widgets during maintenance: 80 widgets/hour * 2 hours = 160 widgets
        Total widgets: 360 + 160 = 520 widgets

    Track Units and Quantities:
    All calculations maintain units in widgets and hours.

9. Verify and Validate Results

    Check for Errors:
        120 * 3 = 360
        80 * 2 = 160
        360 + 160 = 520

    Ensure Compliance:
    The total time accounted for is 5 hours.

    Verify Step By Step:
    Each calculation step logically follows.

10. Ensure Logical Consistency and Coherence

    Confirm Consistency:
    Calculations consistently apply rates and durations.

    Reconcile Contradictions:
    No contradictions found.

11. Play Devil's Advocate

    Challenge Assumptions:
        Verification: What if maintenance duration overlaps with operational hours?
            In this problem, maintenance is clearly within the 5-hour operational window.

    Explore Alternative Perspectives:
    Consider if maintenance affects production beyond rate change, such as temporary halts.

    Test Robustness:
    The solution should hold even if maintenance rates vary slightly.

12. Engage in Socratic Dialogue

    Ask Guiding Questions:
        Are there other factors affecting production rates?
        Is the production rate constant within each phase?

    Facilitate Self-Reflection:
    Reflecting on whether all given data has been utilized appropriately.

13. Synthesize the Final Answer

    Consolidate Insights:
    Production is segmented into two distinct phases with different rates.

    Provide Clear Answer:
    The factory produces a total of 520 widgets over the 5-hour operational period.