
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 trapezoid with $AB$ and $CD$ as bases, and $CD$ twice as long as $AB$. The rectangle is folded along line $EF$ such that vertex $B$ meets point $B'$ on $CD$. Given lengths $AE = 3, EB = 8$, and $FC = 10$, determine the area of trapezoid $ABCD$. Assume that the crease $EF$ is perpendicular to the sides $AD$ and $BC$.

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