
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. $E$ and $F$ are points on $AB$ and $CD$ respectively such that $BE < CF$. If $BCFE$ is folded over $EF$, such that $C$ maps to $C'$ on $AD$ and $B$ maps to $B'$, and $\angle{AB'C'} \cong \angle{B'EA}$. Given $AB' = 7$ and $BE = 17$, compute the area of $ABCD$ 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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