
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
Two regular tetrahedra are inscribed in a cube in such a way that four vertices of the cube serve as the vertices of one tetrahedron, and the remaining four vertices of the cube serve as the vertices of the other. What fraction of the volume of the cube is occupied by the volume of the intersection of these tetrahedra?

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