
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 equation of line $l$ is $y=8$, and the parametric equation of circle $C$ is $\begin{cases} x=2\cos \varphi, \\ y=2+2\sin \varphi \end{cases}(\varphi \text{ is the parameter}).$ Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis.
(I) Find the polar equations of line $l$ and circle $C$;
(II) Ray $OM$: $\theta = \alpha$ (where $0 < \alpha < \frac{\pi }{2}$) intersects circle $C$ at points $O$ and $P$, and intersects line $l$ at point $M$. Ray $ON$: $\theta = \alpha + \frac{\pi }{2}$ intersects circle $C$ at points $O$ and $Q$, and intersects line $l$ at point $N$. Find the maximum value of $\frac{|OP|}{|OM|} \cdot \frac{|OQ|}{|ON|}$.

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