
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 $ABCD$, $AB \parallel CD$, $AB = 5$, $CD = 10$, $BC = 6$, and $AD = 6$. Point $E$ is on line segment $CD$, such that $DE = 2$ times $EC$. Let $\overline{AE}$ be the diagonal. Find the area of $\triangle AEC$.

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