
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 equilateral triangle is inscribed in a circle. Find the ratio of the volumes of the solids obtained from rotating the circle and the triangle around the diameter passing through the vertex of the triangle. Provide the ratio of the smaller volume to the larger volume rounded to two decimal places.

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