
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A convex plywood polygon \( P \) lies on a wooden table. Nails can be driven into the table such that they do not pass through \( P \), but they may touch its boundary. A fixing set is a set of nails that prevents \( P \) from moving on the table. Find the minimum number of nails required to fix any convex polygon.

Present the answer in LaTex format: \boxed{Your answer}
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