
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
Consider a cube with an edge length of 2 units. This cube is cut similarly to the original problem to form several pieces. What is the volume of the piece that contains vertex $W$, if the piece is a pyramid with a rectangular base having sides of lengths 1 unit and 2 units, and with the altitude (W to the base) at 1 unit?

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