
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 $EF$, and $C$ maps to $C'$ on $AD$ and $B$ to $B'$ such that $\angle{AB'C'} \cong \angle{B'EA}$. If $AB' = 8$ and $BE = 10$, find the area of $ABCD$ which can be expressed as $a + b\sqrt{c}$ square units.

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