
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 $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $a=b\cos C+ \dfrac { \sqrt {3}}{3}c\sin B$.  
$(1)$ If $a=2$ and $b= \sqrt {7}$, find $c$;  
$(2)$ If $ \sqrt {3}\sin (2A- \dfrac {\pi}{6})-2\sin ^{2}(C- \dfrac {\pi}{12})=0$, find $A$.

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