
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 $M$ whose base circle radius is the same as the radius of a sphere $O$, if the surface area of cylinder $M$ is equal to that of sphere $O$, then the ratio of their volumes $V_{\text{cylinder}}:V_{\text{sphere}} =$ (Answer in numerical value).

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