
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 vertex $A$ of the tetrahedron $A B C D$ is reflected to $B$, $B$ is reflected to $C$, $C$ is reflected to $D$, and $D$ is reflected to $A$. The points obtained this way are denoted as $A^{\prime}, B^{\prime}, C^{\prime}$, and $D^{\prime}$, respectively. How many times larger is the volume of the tetrahedron $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ compared to the volume of the original tetrahedron $A B C D$?

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