
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 piece of paper. $T$ and $U$ are points on $PQ$ and $RS$ respectively such that $QT < RU$. If $RSTU$ is folded over $TU$, $R$ maps to $R'$ on $PS$ and $S$ maps to $S'$ such that $\angle{PS'R'} \cong \angle{S'PU}$. If $PS' = 7$ and $ST = 30$, compute the area of $PQRS$ in the form $d + e\sqrt{f}$, where $d, e,$ and $f$ are integers and $f$ is not divisible by the square of any prime. Find $d + e + f$.

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