Create an other example application problem that utilizes all the features of this framework:  Prompt Framework

Introduction:

You are an advanced reasoning model designed to employ deliberate, analytical, and methodical reasoning (System 2 Thinking) to solve complex problems effectively. Utilize this capability to understand, analyze, and 

solve the following problem by internally following the structured steps provided. Your goal is to arrive at a clear and accurate solution efficiently.

Structured Reasoning Process

    Comprehend the Problem:
        Read Carefully: Thoroughly read the question to understand the scenario, objectives, and any specific constraints or requirements.
        Identify Key Elements: Note all important data, variables, entities, and their relationships within the problem.

    Organize and Represent Information:
        Gather Data: Extract all relevant information from the problem statement.
        Visualize Relationships: Organize the information using appropriate methods such as lists, tables, diagrams, or equations to clarify relationships and dependencies.

    Determine the Appropriate Approach:
        Select Relevant Concepts: Identify the theories, principles, or formulas applicable to the problem.
        Plan Solution Strategy: Outline the steps or methods needed to solve the problem, considering any specific techniques that are most effective.

    Execute the Solution:
        Perform Calculations: Carry out necessary computations carefully and methodically, ensuring precision at each step.
        Maintain Logical Flow: Ensure each step follows logically from the previous one, and all operations are justified within the context.

    Verify and Reflect:
        Check Accuracy: Review each step and calculation to identify and correct any errors.
        Validate Results: Confirm that the solution meets all the conditions of the problem and is reasonable in context.
        Consider Alternatives (Optional): Reflect on whether there's a more efficient or elegant solution and note any insights.

    Communicate the Solution Clearly:
        Consolidate Findings: Summarize the key steps and results succinctly.
        Present the Final Answer: Provide a clear and unambiguous answer to the question posed, including units or technical terms as appropriate.

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:

    Read Carefully:
        The factory has two production rates due to maintenance.
        Total operation time is 5 hours.

    Identify Key Elements:
        Normal Production Rate: 120 widgets/hour
        Reduced Production Rate: 80 widgets/hour
        Duration at Reduced Rate: 2 hours
        Total Operational Time: 5 hours

2. Organize and Represent Information:

    Time at Normal Rate: 5 hours total - 2 hours reduced = 3 hours

    Table of Production Rates:
    Production Phase 	Rate (widgets/hour) 	Duration (hours)
    Normal Operation 	120 	3
    During Maintenance 	80 	2

3. Determine the Appropriate Approach:

    Relevant Concepts:
        Total Production = Rate × Time
    Solution Strategy:
        Calculate widgets produced during normal operation.
        Calculate widgets produced during maintenance.
        Sum both quantities for total production.

4. Execute the Solution:

    Widgets During Normal Operation:
        ( \text{Widgets}_{\text{normal}} = 120 \text{ widgets/hour} \times 3 \text{ hours} = 360 \text{ widgets} )
    Widgets During Maintenance:
        ( \text{Widgets}_{\text{maintenance}} = 80 \text{ widgets/hour} \times 2 \text{ hours} = 160 \text{ widgets} )
    Total Widgets Produced:
        ( \text{Total Widgets} = 360 \text{ widgets} + 160 \text{ widgets} = 520 \text{ widgets} )

5. Verify and Reflect:

    Check Calculations:
        All multiplications and additions are correct.
    Validate Results:
        The total operational time adds up: 3 hours + 2 hours = 5 hours.
        The production quantities make sense given the rates and times.
    Consider Alternatives:
        Since rates and times are straightforward, no alternative methods are necessary.

6. Communicate the Solution Clearly:

    Final Answer:
        The factory produces 520 widgets over the 5-hour operational period.

Explanation:

By breaking down the operational periods and calculating the production separately, we accurately account for the change in production rate due to maintenance. Summing the widgets produced during each period 

gives us the total production.