
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. Triangle $ABC$ has $\angle BAC = 2 \times \angle ABC$. The perimeter of $\triangle CBD$ is $21$, the perimeter of $\triangle ABC$ is $26$, and the length of $BD$ is $9$. What is the length of $AB$?

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