
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 $xOy$, curve $C_1$: $x+y-4=0$, curve $C_2$: $$\begin{cases} x=\cos\theta \\ y=1+\sin\theta \end{cases}$$ (where $\theta$ is a parameter), establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis.
(I) Find the polar equations of curves $C_1$ and $C_2$;
(II) Ray $l$: $\theta=\alpha$ ($$\rho\geq0, 0<\alpha<\frac{\pi}{2}$$) intersects $C_1$ and $C_2$ at points $M$ and $N$ respectively. Find the maximum value of $\frac{|ON|}{|OM|}$.

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