
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
Points $A, B, C,$ and $D$ lie on a line, in that order, with distances $AB = CD$ and $BC = 15$. Point $E$ is not on the line, and both $BE$ and $CE$ are 13 units long. Additionally, the perimeter of $\triangle AED$ is 1.5 times the perimeter of $\triangle BEC$. Determine $AB$.
A) $9$
B) $\frac{31}{3}$
C) $\frac{34}{3}$
D) $\frac{32}{3}$
E) $11$

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