
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. The lengths of segments $AB$ and $CD$ are equal, and $BC = 15$. Point $E$ is not on the line, and $BE = CE = 12$. The perimeter of $\triangle AED$ is 1.5 times the perimeter of $\triangle BEC$. Determine the length of $AB$.
A) 5.5
B) 6
C) 6.5
D) 7
E) 7.5

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