
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 rectangular prism $ABCD-A^{\prime}B^{\prime}C^{\prime}D^{\prime}$ has dimensions $a$, $b$, $c$ (length, width, height). The intersection of two tetrahedra $AB^{\prime}CD^{\prime}$ and $A^{\prime}DC^{\prime}B$ is a polyhedron $V$. What is the volume of $V$?

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