
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 the parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$ is $V$. Find the volume of the common part of the tetrahedra $A B_{1} C D_{1}$ and $A_{1} B C_{1} D$.

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