
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 there be a line $l$ with an inclination angle $\alpha$ given by $$l: \begin{cases} x=2+t\cos\alpha \\ y= \sqrt {3}+t\sin\alpha \end{cases}$$ (where $t$ is a parameter) that intersects with the curve $$C: \begin{cases} x=2\cos\theta \\ y=\sin\theta \end{cases}$$ (where $\theta$ is a parameter) at two distinct points A and B.  
(1) If $\alpha= \frac {\pi}{3}$, find the coordinates of the midpoint M of 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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