
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 acute triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $2a\sin A(b^{2}+c^{2}-a^{2})=c\sin B(a^{2}+b^{2}-c^{2})+b\sin C(a^{2}+c^{2}-b^{2})$.  
$(1)$ Find the measure of angle $A$;  
$(2)$ If $a=2$, find the range of values for $b+c$.

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