
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 $\triangle ABC$, let $a$, $b$, $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively, and $\frac{b}{\sqrt{3}\cos B}=\frac{c}{\sin C}$. Find:<br/>
$(1)$ The measure of angle $B$;<br/>
$(2)$ If $b=3$, find the range of possible values for the area of $\triangle ABC$.

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