
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 acute triangle $\triangle ABC$, the opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $\cos B + \sqrt{3}\sin B = 2$ and $\frac{\cos B}{b} + \frac{\cos C}{c} = \frac{2\sin A}{\sqrt{3}\sin C}$, find:<br/>
$(1)$ the measure of angle $B$ and the length of side $b$;<br/>
$(2)$ the maximum value of the area of $\triangle ABC$.

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