
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
An inscribed circle is drawn inside an isosceles trapezoid. The distance from the center of the circle to the intersection point of the diagonals of the trapezoid is related to the radius in the ratio of \(3: 5\). Find the ratio of the perimeter of the trapezoid to the length of the inscribed circle.

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