
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 $6 \times 9$ rectangle is rolled to form two different cylinders. Determine the ratio of the larger volume to the smaller volume when the rectangle is used in different orientations.

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