
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. The frustum has a height of 18 centimeters, the area of its lower base is \(144\pi\) sq cm, and the area of its upper base is \(16\pi\) sq cm. Determine the height of the smaller cone that was removed.

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