
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 $SR$ respectively such that $QT < RU$. The sheet is folded over $TU$ such that $S$ maps to $S'$ on $PQ$, and $R$ maps to $R'$ such that $\angle{P'S'R'} = \angle{R'UT}$. Given $P'R' = 8$ and $QT = 26$, determine the area of $PQRS$ and express the area in the form $a + b\sqrt{c}$, where $a, b, c$ 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}
user