
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
Supplementary $4-4$: Coordinate Systems and Parametric Equations

Given that the parametric equations of line $l$ are $\begin{cases} & x=1+\frac{1}{2}t \\ & y=\sqrt{3}+\sqrt{3}t \\ \end{cases}$ (where $t$ is the parameter), and the equation of curve $C$ in the polar coordinate system with the origin as the pole and the non-negative half of the $x$-axis as the polar axis is $\sin \theta - \sqrt{3} \rho \cos^{2} \theta = 0$.

(I) Find the Cartesian equation of curve $C$;

(II) Write out a polar coordinate of the intersection point of line $l$ and curve $C$.

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