
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 equilateral and equiangular convex pentagon of perimeter $2$. Each side of the pentagon is extended to form a five-pointed star. Compute the perimeter of this star by calculating the side lengths of the star segments that join at the extended vertices.
A) $5.236$
B) $6.472$
C) $3.236$
D) $7.472$

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