
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 $\triangle ABC$, given that $\sin ^{2}A+\sin ^{2}B-\sin ^{2}C=2\sin A\sin B(\sqrt{3}-\cos C)$. Find:<br/>
$(1)$ the value of angle $C$;<br/>
$(2)$ if $A=45^{\circ}$ and $BC=2$, find the area of triangle $\triangle ABC$.

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