
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
Trapezoid $ABCD$ has parallel sides $AB = 10$ and $CD = 15$. Diagonals $AC$ and $BD$ intersect at $E$, and diagonal $AC = 13$. If $\triangle AED$ and $\triangle BEC$ have equal areas, find the length of segment $AE$.
A) $\frac{50}{11}$
B) 6
C) $\frac{21}{4}$
D) 5.2
E) $\frac{17}{3}$

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