
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
In the Cartesian coordinate system, take \( n \) points such that no three points are collinear, and color each point either red, green, or yellow, so that the following conditions hold:
(1) In any triangle with all vertices colored red, there is at least one green point inside.
(2) In any triangle with all vertices colored green, there is at least one yellow point inside.
(3) In any triangle with all vertices colored yellow, there is at least one red point inside.

Find the maximum value of the positive integer \( n \).

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