
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
Given trapezoid ABCD with side $\overline{AD}$ perpendicular to side $\overline{DC}$, lengths AD = AB = 3, and DC = 7. Point E is on side $\overline{DC}$ such that $\overline{BE}$ is parallel to $\overline{AD}$, $\overline{BE}$ equally divides DC into sections with segment DE = 3, calculate the area of $\triangle BEC$.

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