
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
Let $PQRS$ be a tetrahedron such that edges $PQ$, $PR$, and $PS$ are mutually perpendicular. Let the lengths of $PQ = a$, $PR = b$, and $PS = c$. If the areas of triangles $PQR$, $PRS$, and $PQS$ are denoted by $u$, $v$, and $w$ respectively, where $u = \frac{1}{2} ab$, $v = \frac{1}{2} bc$, and $w = \frac{1}{2} ca$, find the area of triangle $QRS$.

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