
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 sides opposite to angles $A$, $B$, $C$ in $\triangle ABC$, respectively, and $\dfrac{2b-c}{a} = \dfrac{\cos C}{\cos A}$.
$(1)$ Find the size of angle $A$;
$(2)$ Find the range of the function $y= \sqrt{3}\sin B+\sin \left(C- \dfrac{\pi}{6}\right)$.

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