
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 bases $AB = 10$ and $CD = 15$. Diagonals $AC$ and $BD$ intersect at $E$, with $AC = 17$, and the triangles $\triangle AED$ and $\triangle BEC$ have equal areas. What is the length of $AE$?
A) $\frac{34}{3}$
B) 6
C) $\frac{34}{5}$
D) 7
E) $\frac{37}{5}$

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