
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $\frac{{\sin A + \sin B}}{{\sin C}} = \frac{{c + b}}{{a - b}}$.  
$(1)$ If $a = 2\sqrt{3}$ and $b = 2$, find angle $B$.  
$(2)$ Let $AD$ be the angle bisector of $\angle BAC$ intersecting $BC$ at point $D$. If the area of $\triangle ABC$ is $\sqrt{3}$, find the maximum length of $AD$.

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