
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 $(xOy)$, a curve $C$ has the polar coordinate equation $\rho = \frac{\sin \theta}{\cos^2 \theta}$ with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.

(I) Transform the polar coordinate equation of curve $C$ into a rectangular coordinate equation.

(II) A line $l$ with slope $l$ passes through point $P(0,2)$ and intersects curve $C$ at points $A$ and $B$. Calculate the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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