
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 diameter of a sphere is 6 units and the diameter of a hemisphere is 12 units. Calculate the ratio of the volume of the cylinder (with diameter and height equal to the diameter of the hemisphere) to the combined volume of the sphere and hemisphere.

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