
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 $(xOy)$, given point $P(0,\sqrt{3})$ and curve $C$ with parametric equations $\begin{cases} x=\sqrt{2}\cos\phi \\ y=2\sin\phi \end{cases}\ (\phi\text{ is the parameter})$. Establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of line $l$ is given by $\rho=\frac{\sqrt{3}}{2\cos\left(\theta-\frac{\pi}{6}\right)}$.

(1) Determine the relationship between point $P$ and line $l$, providing the reasons.

(2) Let the two intersection points of line $l$ and curve $C$ be $A$ and $B$, respectively. Find the value of $\frac{1}{|PA|}+\frac{1}{|PB|}$.

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