
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 a convex quadrilateral $ABCD$, side $AB = 12$ and side $CD = 15$. The diagonals $AC$ and $BD$ intersect at point $E$, with the length of diagonal $AC = 18$. If triangles $\triangle AED$ and $\triangle BEC$ have equal areas, find the length of segment $AE$.
A) $\dfrac{72}{5}$
B) $\dfrac{72}{9}$
C) $8$
D) $10$
E) $\dfrac {40}{9}$

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