
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
Inside a right circular cone, a cube is placed such that one edge of the cube lies on the diameter of the base of the cone, the vertices of the cube that do not belong to this edge lie on the lateral surface of the cone, and the center of the cube lies on the height of the cone. Find the ratio of the volume of the cone to the volume of the cube.

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