
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 pyramid with a square base $QRS$ located in the $xy$-plane. Let $P$ be the apex of the pyramid, placed directly above the center of square $QRS$ at a height that equals the side length of the square. Let the areas of triangles $PQR$, $PQS$, and $PRS$ be denoted by $a$, $b$, and $c$, respectively. Find the area of triangle $QRS$ in terms of $a$, $b$, and $c$.

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