
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
$M$ is a set of $n$ points on a plane, satisfying:
(1) There exist 7 points in $M$ that are the vertices of a convex heptagon.
(2) For any 5 points in $M$, if these 5 points are the vertices of 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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