
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 $ABCD$ with $AB \parallel CD$ has $AB = 10$, $CD = 15$, and $AC = 17$. Diagonals $AC$ and $BD$ intersect at $E$. If $\triangle AED$ and $\triangle BEC$ have equal areas, find the length of $AE$.
A) $\frac{32}{5}$
B) $\frac{34}{5}$
C) $\frac{35}{5}$
D) $\frac{36}{5}$
E) $\frac{37}{5}$

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