
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 that the slope angle is $\frac{\pi }{6}$, and the line $l$ passes through the point $P(1,1)$, intersecting the curve $C$: $\begin{cases} & x=2\sin \alpha , \ & y=2+2\cos \alpha \ \end{cases} (\alpha \text{ is a parameter})$ at points $A$ and $B$.

(I) Write the parametric equation of line $l$ and the general equation of curve $C$;

(II) Find the value of $|PA|\cdot|PB|$.

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