
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 was generated by slicing a smaller cone from the top of a larger cone. The larger cone originally had a height of 30 cm before the top was cut off to create the frustum. Now, the frustum that remains has a height of 18 cm and the radius of its upper base is 6 cm, while the radius of its lower base is 10 cm. Determine the altitude of the smaller cone that was cut off.

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