
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
In the rectangular coordinate system $(xOy)$, the curve $C$ has a polar coordinate equation $ρ= \frac{\sin θ}{\cos ^{2}θ}$ with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.
(I) Convert the polar coordinate equation of curve $C$ into a rectangular coordinate equation;
(II) Draw a line $l$ passing through point $P(0,2)$ with a slope of $1$. Find the value of $\frac{1}{|PA|}+ \frac{1}{|PB|}$, where $A$ and $B$ are the intersection points of line $l$ and curve $C$.

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