
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 sides of length 2 units is divided by three segments, each cutting from a vertex on the top face to the midpoint of an edge on the bottom face that isn't directly below it. Focus on the solid that contains the vertex from which all three cuts emanate. What is the volume of this tetrahedron?

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