
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 triangle with sides of 10 cm, 17 cm, and 21 cm rotates around the longest side. Calculate the volume and surface area of the resulting solid of revolution.

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