
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 $f(x)=2\sin \left(x+ \frac {\pi}{3}\right)+\sin x\cos x- \sqrt {3}\sin ^{2}x$.  
$(1)$ If the graph of the function $y=f(x)$ is symmetric about the line $x=a(a > 0)$, find the minimum value of $a$;  
$(2)$ If there exists $x_{0}\in\left[0, \frac {5}{12}\pi\right]$ such that $mf(x_{0})-2=0$ holds, find the range of the real number $m$.

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