
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
When a right triangle is rotated about one leg, the volume of the cone produced is twice the volume produced when rotated about the other leg. The sum of the two volumes is $4480\pi \;\text{cm}^3$. What is the length (in cm) of the hypotenuse of the triangle?

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