
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. The frustum has an altitude of 30 centimeters, the area of its lower base is 400π sq cm and the area of its upper base is 36π sq cm. Find the altitude of the small cone that was cut out.

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