
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 a line $l: \rho\sin(\theta+ \frac {\pi}{3})= \frac { \sqrt {3}}{2}m$, and a 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}
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