
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 divided into several pyramidal pieces. One of the pyramids has its vertex located at the cube’s corner \( V \) and the base is a rectangle that lies on the opposite face of the cube from \( V \). The rectangle has a length of \( \frac{2}{3} \) of the unit cube and a width of \( \frac{1}{2} \) of the unit cube. Calculate the volume of this pyramid.

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