
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
Given an integer  $n\geq 3$ , determine the smallest positive number  $k$  such that any two points in any  $n$ -gon (or at its boundary) in the plane can be connected by a polygonal path consisting of  $k$  line segments contained in the  $n$ -gon (including its boundary). 

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