
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
The triangle with sides \(a\), \(b\), and \(c\) is rotated alternately around each of its sides. Find the ratio of the volumes of the solids obtained in this way.

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