
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 $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $\left(a-c\right)\left(a+c\right)\sin C=c\left(b-c\right)\sin B$.  
$(1)$ Find angle $A$;  
$(2)$ If the area of $\triangle ABC$ is $\sqrt{3}$, $\sin B\sin C=\frac{1}{4}$, find the value of $a$.

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