
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 equation of line $l$ is $y=8$, and the parametric equation of circle $C$ is $$\begin{cases} x=2+2\cos\phi \\ y=2\sin\phi \end{cases}$$ (where $\phi$ is the parameter). A polar coordinate system is established with O as the pole and the non-negative half-axis of the x-axis as the polar axis.  
(1) Find the polar equations of line $l$ and circle $C$;  
(2) 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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