
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 $xOy$, the parametric equation of circle $C$ is $$\begin{cases} x=2\cos\theta \\ y=2\sin\theta\end{cases}$$ ($\theta$ is the parameter), and line $l$ passes through point $P(1,1)$ with an inclination angle of $$\alpha= \frac {\pi}{6}$$,  
(1) Write the parametric equation of line $l$;  
(2) Suppose $l$ intersects circle $C$ at points $A$ and $B$, find the product of the distances from point $P$ to points $A$ and $B$.

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