
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
Five congruent rectangles are placed around a regular pentagon. The area of the outer pentagon formed by this arrangement is $5$ times that of the inner regular pentagon. Each rectangle's shorter side lies against a side of the inner pentagon. If the side length of each side of the inner pentagon is $a$, determine the ratio of the length of the longer side to the shorter side of each rectangle.
A) $\sqrt{5} - 1$
B) $\sqrt{5} + 1$
C) $2\sqrt{5}$
D) $3$

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