
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
Within a cube of side length $a$, a regular tetrahedron is formed by connecting four vertices of the cube such that no two of these vertices belong to the same face. Determine the ratio of the volume of the tetrahedron to the volume of the cube.

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