
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
In tetrahedron $PQRS$, edge $PQ$ has length 5 cm. The area of face $PQR$ is $18 \mbox{cm}^2$ and the area of face $PQS$ is $16 \mbox{cm}^2$. These two faces meet each other at a $45^\circ$ angle. Find the volume of the tetrahedron in $\mbox{cm}^3$.

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