
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 Cartesian coordinate system $xOy$, a point $P(0, -\sqrt{3})$ is given, and the parametric equations of the curve $C$ are $\begin{cases} x = 2\cos\phi \\ y = 2\sin\phi \end{cases}$ (where $\phi$ is the parameter). Establish a polar coordinate system with the origin as the pole and the non-negative half of the $x$-axis as the polar axis. The polar equation of line $l$ is $\rho(\theta + \frac{\pi}{3}) = \frac{3}{2}$.

(I) Determine the relationship between point $P$ and line $l$ and explain the reason.
(II) Suppose line $l$ intersects curve $C$ at two distinct 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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