
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]


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A unit cube is cut three times to form four triangular prisms, three of which are congruent. A vertex $V$ of the original cube is used as the apex for a pyramid, with the base being a triangle formed by three midpoints of adjacent edges of the cube. Calculate the volume of this pyramid.

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