
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 solid sphere is enclosed within a right circular cylinder. The volume of the cylinder is three times that of the sphere. If the height of the cylinder equals the diameter of the sphere, find the ratio of the height of the cylinder to the radius of its base.

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