
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 off the top of a larger cone. The frustum has a height of $18$ cm, the area of its larger base is $324\pi$ sq cm, and the area of its smaller base is $36\pi$ sq cm. Find the height of the smaller cone that was removed.

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