
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 sides of a triangle are \( a = 10 \text{ cm}, b = 15 \text{ cm}, c = 20 \text{ cm} \). What is the volume of the double cone that is formed when the triangle rotates around its longest side?

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