
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 $(xOy)$, let $l$ be a line with an angle of inclination $\alpha$ and $C$ be a curve, both parameterized as follows:

Line $l$: $\begin{cases} x=2+t\cos \alpha \\ y= \sqrt {3}+t\sin \alpha\end{cases}$ ($t$ is the parameter)

Curve $C$: $\begin{cases} x=2\cos \theta \\ y=\sin \theta\end{cases}$ ($\theta$ is the parameter)

Suppose line $l$ intersects curve $C$ at two distinct points $A$ and $B$.

(1) If $\alpha= \dfrac {\pi}{3}$, find the coordinates of the midpoint $M$ of line segment $AB$.

(2) If $|PA|\cdot|PB|=|OP|^{2}$, where $P(2, \sqrt {3})$, find the slope of line $l$.

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