
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
It is known that a circle can be inscribed in a trapezoid with a $60^{\circ}$ angle at the base, and a circle can also be circumscribed around it. Find the ratio of the perimeter of the trapezoid to the length of the inscribed circle. Find the ratio of the perimeter of the trapezoid to the length of the circumscribed circle.

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