
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. If the polar equation of curve $C$ is $\rho\cos^2\theta-4\sin\theta=0$, and the polar coordinates of point $P$ are $(3, \frac{\pi}{2})$, in the Cartesian coordinate system, line $l$ passes through point $P$ with a slope of $\sqrt{3}$.

(Ⅰ) Write the Cartesian coordinate equation of curve $C$ and the parametric equation of line $l$;

(Ⅱ) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $\frac{1}{|PA|}+ \frac{1}{|PB|}$.

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