
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
Convex quadrilateral $ABCD$ has $AB = 15$ and $CD = 20$. Diagonals $AC$ and $BD$ intersect at $E$, $AC = 18$, and $\triangle AED$ and $\triangle BEC$ have equal areas. What is $AE$?
A) $\frac{42}{7}$  
B) $\frac{54}{7}$  
C) $\frac{48}{7}$  
D) $\frac{60}{7}$  
E) $\frac{66}{7}$

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