
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
Given a line $l$ passes through the 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 the circle $x^{2}+y^{2}=4$ at two 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}
user