
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
In the Cartesian coordinate system $xOy$, we have a line $l$ with the polar equation $\rho\sin \left(\theta+ \frac{\pi}{3}\right)= \frac{\sqrt{3}}{2}m$, and a curve $C$ with the parametric equations $\begin{cases} x=1+\sqrt{3}\cos \theta \\ y=\sqrt{3}\sin \theta \end{cases}$ (where $\theta$ is the parameter).
$(1)$ Find the rectangular coordinate equation of line $l$ and the ordinary equation of curve $C$;
$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, if $|AB| \geqslant 3$, find the range of values for the real number $m$.

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