
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
Let ABCDE be an equiangular but not necessarily equilateral convex pentagon with a perimeter of 2. Each side length can vary while maintaining a constant perimeter. Determine the difference between the maximum and minimum possible values of the perimeter, s, of the five-pointed star polygon formed by the pairwise intersections of lines that extend the sides of this pentagon.

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