Chain of Thought Problem Solver

Solve this problem using rigorous step-by-step reasoning:

1) First, restate the problem in your own words to confirm understanding
2) Identify what information you have and what you need
3) Show your reasoning at each step — explain WHY, not just WHAT
4) If you're uncertain about any step, explicitly say so and explain your confidence level
5) Consider edge cases and potential pitfalls
6) After reaching your solution, verify it by working backwards
7) Rate your confidence in the answer (low/medium/high) and explain why

Problem: {{problem}}