
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 is cut forming a pyramid piece that contains the vertex W, with the base of the pyramid lying on the opposite face of W. The base of the pyramid is a rectangle and not a square as before, with the length of one side of the rectangle being 1/3 of the side of the cube and the other side being 1/4 of the side of the cube. If the side of the cube is 1 unit, what is the volume of this pyramid that contains vertex W?

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