
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 $AB = 10$ and $CD = 15$. Diagonals $AC$ and $BD$ intersect at $E$, where $AC = 18$, and $\triangle AED$ and $\triangle BEC$ have equal perimeters. Calculate the length of $AE$.
**A)** $6$  
**B)** $7.2$  
**C)** $7.5$  
**D)** $9$  
**E)** $10$

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