
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
Regular tetrahedron  $ABCD$  has center  $O$  and side length  $1$ . Points  $A'$ ,  $B'$ ,  $C'$ , and  $D'$  are defined by reflecting  $A$ ,  $B$ ,  $C$ , and  $D$  about  $O$ . Compute the volume of the polyhedron with vertices  $ABCDA'B'C'D'$ .

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