
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
Given a regular octahedron $O$ with side length $s$, find the tetrahedron $T$ such that each vertex of $T$ is at the center of a face of $O$. If the volume of $O$ is four times that of $T$, and if $s = 2\sqrt{2}$, find the volume of $T$.

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