
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 $ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, $S$ is the area of the triangle, and it is given that $\frac{\cos B}{\cos C} = -\frac{b}{2a+c}$  
$(1)$ Find the measure of $\angle B$;  
$(2)$ If $a=4$ and $S=5\sqrt{3}$, find the value of $b$.

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