
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]


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A large regular tetrahedron's vertices are shifted to $(1,1,0,0)$, $(0,1,1,0)$, $(0,0,1,1)$, and $(1,0,0,1)$ in four-dimensional space. Calculate the ratio of the volume of a smaller tetrahedron formed by the centers of these faces compared to the volume of the larger tetrahedron.

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