
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, the parametric equations of the curve $C$ are given by $\begin{cases} x=\sqrt{5}\cos\phi \\ y=\sqrt{15}\sin\phi \end{cases}$ where $\phi$ is the parameter. Establish a polar coordinate system with the origin as the pole and the positive half of the $x$-axis as the polar axis. Let $P(\sqrt{3}, \frac{\pi}{2})$ be a point and $l$ be a line with the polar equation $\rho=\frac{\sqrt{3}}{2\cos(\theta-\frac{\pi}{6})}$.
(1) Determine the relationship between point $P$ and line $l$, and explain the reasons.
(2) Suppose the two intersection points of line $l$ and curve $C$ are $A$ and $B$. Calculate the value of $|PA|\cdot|PB|$.

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