
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
$PQRS$ is a rectangular sheet of paper. $T$ and $U$ are points on $PQ$ and $RS$ respectively such that $QT < PU$. The rectangle $PQTU$ is folded over $TU$, mapping $Q$ to $Q'$ on $PS$ and $P$ to $P'$ such that $\angle{P'Q'S}$ is a right angle. If $PQ' = 8$ and $QT = 36$, find the area of rectangle $PQRS$ which can be expressed as $a + b\sqrt{c}$ square units, where $a, b, $ and $c$ are integers and $c$ is not divisible by the square of any prime. Compute $a + b + c$.

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