
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
All segments of a closed $n$-sided polyline (possibly self-intersecting, but "non-degenerate" such that all vertices of the polyline are distinct and all segments belong to different lines) are equal to 1.

a) What is the minimum possible value of the diameter of the polyline if $n=2,3,4,5,6$?

b) For which $n$ can the diameter of the polyline be equal to 1? For which $n$ can it not be equal to 1, but can be arbitrarily close to 1?

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