
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). Taking 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, and convert the polar equation of curve $C$ into a standard equation;  
(2) Find the polar coordinates of the intersection points of line $l$ and curve $C$ ($\rho\geq0$, $0\leq\theta<2\pi$).

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