
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
The volume of a truncated cone circumscribed around a sphere is twice the volume of the inscribed sphere. By how many times is the radius of the base circle of the truncated cone the radius of the top circle's radius?

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