
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 to the internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $\left(b-c\right)\sin B=b\sin \left(A-C\right)$.  
$(1)$ Find angle $A$;  
$(2)$ If $\triangle ABC$ is an acute triangle and the area of $\triangle ABC$ is $S$, find the range of $\frac{{a^2}+{b^2}+{c^2}}{S}$.

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