
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 the diagram, triangles \(ABC\) and \(CBD\) are isosceles, the perimeter of \(\triangle CBD\) is 19, the perimeter of \(\triangle ABC\) is 20, and the length of \(BD\) is 7. Find the length of \(AB\).

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