
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 set of finitely many points \( M \) on the plane satisfies:
(a) Any three points are not collinear;
(b) Each point in \( M \) can be colored either red or blue in such a way that every triangle formed by any three points of the same color has at least one point of the other color inside it.

What is the maximum possible number of points in \( M \)?

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