
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 obtained by cutting the top smaller cone from a larger cone. The frustum has an altitude of $30$ centimeters. If the area of its lower base is $400\pi$ square centimeters and the area of its upper base is $36\pi$ square centimeters, determine the altitude of the small cone that was removed.

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