
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
A cube is inscribed in a regular quadrilateral pyramid in such a way that one edge of the cube lies on the midline of the base of the pyramid. The vertices of the cube, which do not belong to this edge, lie on the lateral surface of the pyramid. The center of the cube lies on the height of the pyramid. Find the ratio of the volume of the pyramid to the volume of the cube.

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