
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
Tetrahedron $PQRS$ has $PQ=6$, $PR=4$, $PS=5$, $QR=5$, $QS=3$, and $RS=4\sqrt{2}$. Find the volume of the tetrahedron.
A) $\frac{1}{3}$
B) $\frac{\sqrt{2}}{6}$
C) $\frac{\sqrt{3}}{9}$
D) $\frac{\sqrt{6}}{9}$
E) $\frac{2\sqrt{2}}{9}$

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