
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
The base radius of a right circular cone is $25 \mathrm{~cm}$, and its slant height is $42 \mathrm{~cm}$. This cone needs to be cut by a plane parallel to the base such that the volumes of the two resulting parts are equal. What is the radius of the circular intersection, and what is the height of the smaller cone?

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