
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 off of a larger cone. The frustum has an altitude of 30 centimeters, the area of its lower base is $400\pi$ square centimeters, and the area of its upper base is $100\pi$ square centimeters. What is the altitude of the small cone that was cut off, and what was the total height of the original cone?

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