
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
In trapezoid $ABCD$, $\overline{AD}$ is perpendicular to $\overline{DC}$, $AD = AB = 5$, and $DC = 10$. Additionally, $E$ is on $\overline{DC}$ such that $\overline{BE}$ is parallel to $\overline{AD}$. Find the area of the parallelogram formed by $\overline{BE}$.

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