
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 $\triangle ABC$, $\sin ^{2}A-\sin ^{2}B=\sin C\left(\sin C-\sin B\right)$.  
$(1)$ Find $A$;  
$(2)$ If point $D$ is on side $BC$ with $BD=CD=\sqrt{3}$ and $AD=\sqrt{7}$, find the area of $\triangle ABC$.

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