
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 can be rolled to form two different cylinders. Determine the ratio of the volume of the cylinder with the larger volume to the cylinder with the smaller volume when one cylinder is formed by using 6 as the height and the other using 9 as the height.

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