
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 $C$: $\begin{cases} x = 1 + \sqrt{3} \cos \theta \\ y = \sqrt{3} \sin \theta \end{cases} (\theta \text{ is a parameter})$,

(1) Determine the relationship between the line $l$ and the curve $C$ when $m = 3$;

(2) Find the range of the real number $m$ if there exists a point on the curve $C$ that is equidistant to the line $l$ with a distance of $\frac{\sqrt{3}}{2}$.

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