
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 $(xOy)$, there is a line $l$: $\begin{cases} x=2+t \\ y=2-t \end{cases}$ ($t$ is a parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive $x$-axis as the polar axis. There is a curve $C$: $\rho =2\sin \theta$.

(1) Find the polar coordinate equation of line $l$ and the Cartesian coordinate equation of curve $C$;

(2) Let ray $\theta = \alpha$ ($\rho \geqslant 0, 0 < \alpha < \frac{\pi}{2}$) intersect with line $l$ and curve $C$ at points $M$ and $N$ (excluding point $O$), respectively. Find the maximum value of $\frac{|ON|}{|OM|}$.

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