
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
$ABCD$ is a rectangular sheet of paper. Points $E$ and $F$ are on $AB$ and $CD$, respectively, with $BE < CF$. The rectangle is folded over line $EF$ such that point $C$ maps to $C'$ on $AD$ and point $B$ maps to $B'$ on $AD$. Given that $\angle{AB'C'} \cong \angle{B'EA}$, $AB' = 7$, and $BE = 25$, compute the area of rectangle $ABCD$, expressed in the form $a + b\sqrt{c}$, where $a, b, c$ are integers and $c$ is not divisible by the square of any prime.

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