
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 cylinder and a sphere, the radii of the base of the cylinder and the great circle of the sphere are equal. The ratio of the total surface area of the cylinder to the surface area of the sphere is $m: n$. Find the ratio of their volumes.

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