
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 parametric equation of line $l$ is
$$
\begin{cases}
x=1+\frac{1}{2}t \\
y=\sqrt{3}+\sqrt{3}t
\end{cases}
\quad (t\text{ is the parameter})
$$
With the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar coordinate system is established, and the equation of curve $C$ is $\sin\theta-\sqrt{3}\rho\cos^2\theta=0.$  

(I) Find the Cartesian coordinate equation of curve $C$;  
(II) Provide one set of polar coordinates for the point of intersection between line $l$ and curve $C$.

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