
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 $a$, $b$, and $c$ be the lengths of the sides opposite angles $A$, $B$, and $C$, respectively. It is known that $\sqrt{3}c=\sqrt{3}bcosA+asinB$.  
$(1)$ Find the measure of angle $B$.  
$(2)$ When $a=2\sqrt{2}$ and $b=2\sqrt{3}$, find the lengths of side $c$ and the area $S$ of $\triangle ABC$.

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