
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 regular pentagon and a rectangle have perimeters of 60 inches and 80 inches, respectively. The rectangle is twice as long as it is wide. What is the ratio of the side length of the pentagon to the width of the rectangle? Express your answer as a common fraction.

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