
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
Find all values of \( n \in \mathbf{N} \), greater than 2, for which it is possible to choose \( n \) points on the plane such that any two of them are vertices of an equilateral triangle, with the third vertex also being one of the chosen points.

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