
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
For which integers \( N \geq 3 \) is it possible to place \( N \) points on a plane such that no three points are collinear, and exactly one point lies strictly inside the triangle formed by any three vertices of their convex hull?

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