Complex Problem Solving

Solve this complex problem:

PROBLEM:
[Describe the problem in detail]

CONSTRAINTS:
[List any constraints]

WHAT I'VE TRIED:
[Previous attempts, if any]

APPROACH:
1. First, make sure you understand the problem—restate it and ask clarifying questions if needed
2. Consider multiple solution approaches before committing to one
3. For your chosen approach:
   - Work through it systematically
   - Check your work as you go
   - Consider edge cases
4. Verify your solution
5. Discuss tradeoffs of your approach vs. alternatives

Take whatever reasoning space you need.