
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. One of the pieces is a pyramid with a rectangular base. The vertices of the pyramid are $V, W, X, Y, Z$, where $VWXYZ$ forms the base rectangle with lengths $1$ and $1/4$. The pyramid's height from vertex $V$ (at one corner of the cube) to the apex $P$ (directly above $V$ inside the cube) is $1$. Calculate the volume of this pyramid.

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