
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 $xOy$, the parametric equation of line $l$ is $\begin{cases} x=2+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t\end{cases}$ (where $t$ is the parameter). With the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of curve $C$ is: $\rho=4\cos \theta$.  
$(1)$ Convert the parametric equation of line $l$ into a polar equation;  
$(2)$ Find the polar coordinates of the intersection points of line $l$ and curve $C$ $(\rho\geqslant 0,0\leqslant \theta < 2\pi)$.

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