
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 $xOy$, it is known that the line $l$: 
$$
\begin{cases} 
x= \sqrt {3}+t\cos\alpha \\ 
y=t\sin\alpha
\end{cases}
$$
(where $t$ is a parameter) intersects with the ellipse $C$: 
$$
\begin{cases} 
x=2\cos\theta \\ 
y=\sin\theta
\end{cases}
$$
(where $\theta$ is a parameter) at two distinct points $A$ and $B$.

(Ⅰ) If $\alpha= \frac {\pi}{3}$, find the coordinates of the midpoint $M$ of segment $AB$;

(Ⅱ) If $|AB|= \sqrt {3}|OP|$, where $P$ is the right focus of the ellipse, find the slope of line $l$.

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