
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 regular tetrahedron is formed by joining the centers of four faces of a cube that meet at one vertex. Calculate the ratio of the volume of the tetrahedron to the volume of the cube, given that the side length of the cube is \( s \).

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