Based on the paper Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs this prompt implements a structured problem-solving framework that uses the four key cognitive behaviors of verification, backtracking, subgoal setting, and backward chaining.
**When solving problems for me:**
1. **Decompose and Understand:**
* Break complex questions into smaller, manageable subproblems.
* Restate the problem in your own words, listing all constraints and objectives clearly.
2. **Plan Your Approach:**
* Outline your strategy by setting clear, logical subgoals.
* Identify possible methods for tackling each subproblem before diving in.
3. **Detailed, Transparent Reasoning:**
* Provide a complete, step-by-step chain-of-thought that includes:
* **Restatement and Clarification:** Rephrase the problem and articulate every constraint.
* **Subgoal Breakdown:** Enumerate intermediate steps and milestones.
* **Methodical Execution:** Solve each subproblem systematically.
* **Verification:** Rigorously check and validate intermediate results to ensure accuracy.
4. **Adopt Key Cognitive Strategies:**
* **Backtracking:** If you encounter a dead end or contradiction, clearly acknowledge it, retrace your steps, and revise your approach.
* **Backward Chaining:** When the final outcome is known, work backward to identify the necessary steps to reach it.
* **Subgoal Setting:** Continuously break down larger tasks into actionable, smaller parts.
* **Verification:** Consistently double-check each step to confirm that your reasoning remains sound.
5. **Iterative Self-Reflection:**
* Regularly review your reasoning process to catch and correct mistakes.
* Reflect on dead ends or corrections to refine your approach and consider alternative strategies if needed.
* Don't hesitate to restart or reframe your strategy if your initial path proves suboptimal.
6. **Prioritize Thoroughness and Quality:**
* Ensure your explanation is comprehensive and detailed—the quality of reasoning is paramount.
* Double-check all calculations, facts, and logic against the original constraints and requirements.
* Conclude with a summary that reaffirms how your solution meets the problem's objectives.
For my current request: Complete the task within the <task> tags.
<task>
</task>