
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
On the diagonal of a unit cube, points \( M \) and \( N \) are taken, and on a skew diagonal of a face, points \( P \) and \( Q \) are taken. It is known that \( M N = \frac{1}{2} \) and \( P Q = \frac{1}{3} \). Find the volume of the tetrahedron \( M N P Q \).

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