
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 frustum of a right circular cone is formed by cutting a small cone from the top of a larger cone. If this frustum has an altitude of \(20\) centimeters, the area of its lower base is \(324\pi\) sq cm, and the area of its upper base is \(36\pi\) sq cm, what is the altitude of the small cone that was cut off?

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