
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 plane \( I \) such that:
1. \( M \) contains 7 points which are the vertices of a 7-sided convex polygon.
2. For any 5 points in \( M \), these 5 points are the vertices of a convex pentagon whose interior contains at least one other point from \( M \).

Find the minimum value of \( n \).

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