
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 plane $(xOy)$, the parametric equation of circle $C$ is $\begin{cases} x=4\cos \theta \\ y=4\sin \theta \end{cases}(\theta \text{ is the parameter})$, and line $l$ passes through point $P(1,2)$ with an angle of inclination $\alpha= \frac {\pi}{6}$.
(1) Find the parametric equation of line $l$;
(2) Suppose line $l$ intersects circle $C$ at points $A$ and $B$, find the value of $|PA|\cdot|PB|$.

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