
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
Let the three internal angles $A$, $B$, and $C$ of $\triangle ABC$ have opposite sides $a$, $b$, and $c$ respectively, and it is given that $b(\sin B-\sin C)+(c-a)(\sin A+\sin C)=0$.

$(1)$ Find the size of angle $A$;

$(2)$ If $a=\sqrt{3}$ and $\sin C=\frac{1+\sqrt{3}}{2}\sin B$, find the area of $\triangle ABC$.

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