
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 $\begin{cases}x=4\cos θ \\\\ y=4\sin θ\end{cases}$, and line $l$ passes through point $P(2,2)$ with a slope angle $\alpha =\dfrac{\pi }{3}$. Line $l$ intersects circle $C$ at points $A$ and $B$.

(I) Write the standard equation of the circle and the parametric equation of line $l$.
(II) Calculate $| PA |\cdot | PB |$.

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