
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
In a regular tetrahedron whose vertices are located at the points (1,0,0), (0,1,0), (0,0,1), and (0,0,0), find the centers of the four faces and form a new smaller tetrahedron using these centers. Calculate the ratio of the volume of this smaller tetrahedron to the original tetrahedron.

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