
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 $7 \times 12$ rectangle is used to form two different cylinders. Determine the ratio of the volumes of the larger cylinder to the smaller cylinder when the rectangle is rolled along its longer side and then along its shorter side.

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