
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
Given \( n \) special points on a plane with no three points being collinear, each point is either red, green, or yellow, and they satisfy the following conditions:
1. Inside any triangle whose vertices are all red, there is at least one green point.
2. Inside any triangle whose vertices are all green, there is at least one yellow point.
3. Inside any triangle whose vertices are all yellow, there is at least one red point.
Find the maximum possible integer value of \( n \).

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