
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 that $a$, $b$, $c$ are the opposite sides of angles $A$, $B$, $C$ in triangle $\triangle ABC$, and $a\cos B+\sqrt{3}a\sin B-b-c=0$.  
$(1)$ Find the value of angle $A$;  
$(2)$ If the area of acute triangle $\triangle ABC$ is $\sqrt{3}$, find the range of values for $b$.

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