
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 equations of line $l$ as $\begin{cases} & x=1+\frac{1}{2}t \\ & y=\sqrt{3}+\sqrt{3}t \\ \end{cases}$ ($t$ is the parameter), establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The equation of the curve $C$ is given by $\sin \theta -\sqrt{3}\rho {\cos ^{2}}\theta =0$.

(1) Find the Cartesian equation of the curve $C$.
(2) Write the polar coordinates of one of the intersection points of line $l$ and curve $C$.

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