
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
Given the conditions:①$a\cos B-b\cos A=c-b$, ②$tanA+tanB+tanC-\sqrt{3}tanBtanC=0$, ③${S_{\triangle ABC}}=\frac{1}{2}a({b\sin B+c\sin C-a\sin A})$, choose one of these three conditions and answer the following questions.<br/>In $\triangle ABC$, where the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and _____.<br/>$(1)$ Find angle $A$;<br/>$(2)$ If $a=8$, the radius of the incircle of $\triangle ABC$ is $\sqrt{3}$, find the area of $\triangle ABC$.

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