
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 created by cutting a smaller cone from a larger cone. If the frustum has an altitude of 30 centimeters, with the area of the lower base being 400π square centimeters, and the area of the upper base being 100π 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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