
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 cube with a side length of 2 units is sliced along a diagonal plane that intersects three major vertices, A, B, and D, forming a tetrahedral piece removed from the original cube. Another slice is made that intersects the center of the tetrahedral piece and the center of the remaining part of the cube, effectively forming a smaller tetrahedral piece within the original one. Determine the volume of this smaller, inner tetrahedron.

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