
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 $xOy$, point $P(0,\sqrt{3})$ is given. The parametric equation of curve $C$ is $\begin{cases}x= \sqrt{2}\cos \phi \\ u=2\sin \phi\end{cases}$ (where $\phi$ is the parameter). With the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of line $l$ is $\rho=\dfrac{\sqrt{3}}{2\cos \left( \theta -\dfrac{\pi }{6} \right)}$.

$(1)$ Determine the positional relationship between point $P$ and line $l$ and explain the reason;

$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, calculate the value of $\dfrac{1}{\left| PA \right|}+\dfrac{1}{\left| PB \right|}$.

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