
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
Given a solid cube, we want to carve a cone out of it such that the cone's axis coincides with one of the cube's body diagonals, and the volume of the cone is as large as possible. Express the dimensions of the cone in terms of the cube's edge length.

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