
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
A coordinate system $xOy$ is given in the plane, where the slope angle of the line $l$ is $α$, and the equation of the line $l$ is $$\begin{cases} & x=2+t\cos α \\ & y=\sqrt{3}+t\sin α \end{cases}$$ where $t$ is a parameter. A polar coordinate system is established with $O$ as the pole and the non-negative semiaxis of the $x$-axis as the polar axis. The polar equation of the curve $C$ is ${{\rho }^{2}}=\dfrac{4}{1+3{{\sin }^{2}}\theta }$. The line $l$ intersects the curve $C$ at two distinct points $A$ and $B$.
(1) If $α=\dfrac{\pi }{3}$, find the rectangular coordinates of the midpoint $M$ of the segment $AB$;
(2) If $|PA|\cdot |PB|=|OP|^{2}$, where $P(2,\sqrt{3})$, find the slope of the line $l$.

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