
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 $7 \times 10$ rectangle is used to form two different cylindrical shapes by rolling it along its length and width. Calculate the ratio of the larger volume to the smaller volume when the rectangle is formed into cylinders in these two ways. Express your answer as a common fraction.

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