
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 $D$ are arranged consecutively on a straight line with $AB = CD$ and $BC = 15$. Point $E$ is not on the line, and $BE = CE = 13$. The perimeter of $\triangle AED$ is twice the perimeter of $\triangle BEC$. Find the value of $AB$.

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