
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
Given that in triangle $\triangle ABC$, the opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and the radius of the circumcircle of $\triangle ABC$ is $R$, and $2R-b=2b\sin B$, where $0<B<\frac{π}{2}$. Find:<br/>
$(1)$ the value of $B$;<br/>
$(2)$ if $a=\sqrt{3}$ and $c=3$, find $\sin C$.

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