
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
Given a right circular cone and a sphere have volumes related such that the volume of the cone is one-third that of the sphere, and the radius of the base of the cone is twice the radius of the sphere, determine the ratio of the altitude of the cone to the radius of its base.

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