
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 $BE < CF$. The rectangle is folded over the line $EF$ (not necessarily at the midpoint), and when folded, point $C$ maps to $C'$ on $AD$ and $B$ maps to $B'$. It is known that $\angle{AB'C'} \cong \angle{B'EA}$, $AB' = 6$, and $BE = 24$. If the length $AD$ is three times $AB'$, find the area of rectangle $ABCD$. Assume $AB' = C'D$ after folding.

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