
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
Let \( M \) be a set of \( n \) points in the plane such that:
1. There are 7 points in \( M \) that form the vertices of a convex heptagon.
2. For any 5 points in \( M \), if these 5 points form a convex pentagon, then the interior of this convex pentagon contains at least one point from \( M \).

Find the minimum value of \( n \).

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