
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
We inscribe a cone with an equal base into a sphere with a radius of $R$. A plane parallel to the base of this cone is placed. For which position of the plane will the sum of the intersections of the cone and the sphere be maximal?

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