
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 unit cube is cut into several pieces by making a diagonal cut across one face and then extending this plane through the opposite vertex. Determine the volume of the pyramid with a vertex at one corner of the cube and a triangular base formed by the midpoint of three adjacent edges of the cube.

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