
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 $9 \times 12$ rectangle can be used to form two different cylinders by rolling along its length or width respectively. What is the ratio of the larger volume to the smaller volume when formed? Express your answer as a common fraction.

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