
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 is rotated about one of its legs, creating a cone with a volume of $1620\pi \;\textrm{ cm}^3$. Rotating the triangle about the other leg produces a cone with a volume of $3240\pi \;\textrm{ cm}^3$. Determine the length (in cm) of the hypotenuse of this triangle.

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