
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
A convex quadrilateral $ABCD$ has $AB = 10$, $CD = 15$, and diagonals $AC = 17$. Diagonals $AC$ and $BD$ intersect at $E$. If the ratio of the areas of triangles $\triangle AED$ to $\triangle BEC$ is the same as the ratio of $AB$ to $CD$, find the length of $AE$.
A) $\frac{34}{5}$  
B) $7$  
C) $\frac{39}{5}$  
D) $8$

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