
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
A regular tetrahedron has edge lengths of 2. A smaller cube is placed inside the tetrahedron such that its bottom face is parallel and coincident with one of the triangular faces of the tetrahedron. Each vertex of the top face of the cube touches a different face of the tetrahedron. What is the maximum volume of this cube?
**A)** $\frac{8}{243}$
**B)** $\frac{8\sqrt{3}}{243}$
**C)** $\frac{2\sqrt{2}}{243}$
**D)** $\frac{2\sqrt{3}}{243}$
**E)** $\frac{\sqrt{3}}{243}$

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