
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
$N$ points on a plane, none of which are collinear, are pairwise connected with segments (each with each). Some of the segments are colored red, and the others blue. All red segments form a closed non-self-intersecting polygonal chain, and all blue segments do too. Find all possible values of $N$ for which this arrangement is possible.

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