
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 convex pentagon with a perimeter of 2. The extensions of the sides of this pentagon intersect to form a five-pointed star. Let $s$ be the perimeter of this star. Calculate $s$.
A) $\frac{1}{2} \sec 72^\circ$
B) $1 \sec 72^\circ$
C) $\frac{3}{2} \sec 72^\circ$
D) $2 \sec 72^\circ$

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