
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
In triangle \(ABC\), the bisectors \(BL\) and \(AE\) of angles \(ABC\) and \(BAC\) respectively intersect at point \(O\). It is known that \(AB = BL\), the perimeter of triangle \(ABC\) is 28, and \(BO = 2OL\). Find \(AB\).

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