
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 rectangular coordinate system $(xOy)$, the parametric equation of circle $C$ is $\begin{cases}x=4\cos \theta \\\\ y=4\sin \theta\end{cases} (\theta$ is the parameter$)$, and line $l$ passes through point $P(1,2)$ with a slope angle $a=\frac{\pi}{6}$.

(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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