
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
At what distance from the center must a sphere of radius $R$ be cut by a plane so that the volume of the smaller spherical cap equals the volume of the cone whose base is the cap's base and whose apex is at the center of the sphere?

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