
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
In convex quadrilateral $ABCD$, we have $AB = 6$, $CD = 15$, $AC = 13$, and diagonals $AC$ and $BD$ intersect at $E$. It is known that angle $AEB = angle CED$. What is the length of $AE$?
A) $\frac{12}{5}$
B) $4$
C) $\frac{27}{7}$
D) $\frac{28}{7}$
E) $\frac{26}{7}$

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