
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
The volume of a regular tetrahedron \( ABCD \) is 1, and \( O \) is its center. The regular tetrahedron \( A'B'C'D' \) is symmetrical to \( ABCD \) with respect to the point \( O \). Determine the volume of the common part of these two regular tetrahedrons.

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