
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
In a certain convex \(n\)-gon (\(n > 3\)), all distances between vertices are distinct.

a) We call a vertex uninteresting if the closest vertex to it is a neighboring one. What is the minimum possible number of uninteresting vertices (for a given \(n\))?

b) We call a vertex unusual if the farthest vertex from it is a neighboring one. What is the maximum possible number of unusual vertices (for a given \(n\))?

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