
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 sphere is perfectly fitted inside a truncated right circular cone. The volume of the truncated cone is three times that of the sphere. Determine the ratio of the radius of the larger base (bottom) of the truncated cone to the radius of the smaller base (top) of the truncated cone.

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