
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 the function $f(x)=\sin x+\cos \left(x- \dfrac {\pi}{6}\right)$, where $x\in\mathbb{R}$.  
$(1)$ Find the maximum value of $f(x)$;  
$(2)$ In triangle $ABC$, the sides opposite angles $A$ and $B$ are $a$ and $b$ respectively. If $B=2A$ and $b=2af\left(A- \dfrac {\pi}{6}\right)$, find the magnitude of angle $C$.

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