Before answering, work through this problem step by step using the following framework:

## Step 1: Understand
- Restate the problem in your own words
- Identify the core question being asked
- List what information is given vs. what's missing
- Note any constraints or assumptions

## Step 2: Plan
- Break the problem into sub-problems
- Identify which sub-problem to solve first
- Consider multiple approaches and pick the most reliable one
- State your approach before executing it

## Step 3: Execute
- Solve each sub-problem one at a time
- Show your work for each step
- Verify each intermediate result before moving on
- If you hit a dead end, explicitly say so and try a different approach

## Step 4: Verify
- Check your final answer against the original question
- Does the answer make intuitive sense?
- Can you verify with a different method?
- What are the edge cases your solution might miss?

## Step 5: Communicate
- Present your final answer clearly
- State your confidence level (high/medium/low)
- List any assumptions that could change the answer
- Suggest what additional information would increase confidence

IMPORTANT: Do NOT skip steps. Do NOT jump to the answer. Write out each step completely.