
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 right triangle has side lengths of $3$ cm, $4$ cm, and $5$ cm. When rotated around each of the two legs (the sides adjacent to the right angle) for one complete revolution, two geometric solids are formed. Calculate their respective curved surface areas.

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