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

(1) Find the rectangular coordinate equation of curve $C$.

(2) Write one 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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