
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
Sam and Chris each start with a sheet of paper. Sam has a sheet that measures 7 inches by 10 inches, and Chris has a sheet that measures 9 inches by 12 inches. Each of them rolls their paper sheet to form a cylindrical tube. Sam tapes the two 10-inch sides together without overlap, and Chris tapes the two 9-inch sides together without overlap. What is $\pi$ times the positive difference in the volumes of the two tubes?

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