
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
On a coordinate plane, choose \( n \) points such that no three points are collinear, and color each of these points one of three colors: red, green, or yellow. The points must satisfy the following three conditions:
1. In any triangle formed by three red points, there is at least one green point inside the triangle.
2. In any triangle formed by three green points, there is at least one yellow point inside the triangle.
3. In any triangle formed by three yellow points, there is at least one red point inside the triangle.
Find the maximum value of the positive integer \( n \).

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