
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 line $l$: $\rho\sin (\theta+ \frac {\pi}{3})= \frac { \sqrt {3}}{2}m$, and the curve $C$: 
$$
\begin{cases} 
x=1+ \sqrt {3}\cos \theta \\
y= \sqrt {3}\sin \theta
\end{cases}
$$
$(1)$ When $m=3$, determine the positional relationship between line $l$ and curve $C$;  
$(2)$ If there exists a point on curve $C$ that is at a distance of $\frac { \sqrt {3}}{2}$ from line $l$, find the range of the real number $m$.

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