
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 $a$, $b$, $c$, _____. Choose one of the following two conditions to fill in the blank and solve:  
① $2\cos A\left(c\cos B+b\cos C\right)=a$;  
② $\sqrt{3} \sin C - b = c - a\cos C$.  
$(1)$ Find angle $A$;  
$(2)$ If $\triangle ABC$ is an acute triangle, find the range of $\frac{bc-c^{2}}{{a}^{2}}$.  
Note: If multiple conditions are chosen for the solution, the first one will be scored.

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