
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
Rotate a right triangle - with legs $a$ and $b$, and hypotenuse $c$ - around lines passing through its vertices and parallel to the opposite sides. Calculate the surface area and volume of the 3 resulting solids of revolution. What is the ratio of the surface areas and volumes of the 3 solids in the case when $a = b$?

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