
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
A closed five-segment line forms an equiangular star. What is the perimeter of the inner pentagon \(ABCDE\) if the length of the initial broken line is 1?

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