
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 opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and $\left(2c+b\right)\cos A+a\cos B=0$, with $a=\sqrt{3}$.  
$(1)$ Find the measure of angle $A$.  
$(2)$ Find the range of values for $2b+c$.

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