
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 $x=2$, and the parametric equations of curve $C$ are given by $\begin{cases} x=\cos \alpha \\ y=1+\sin \alpha \end{cases}$ ($\alpha$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis.

(I) Find the polar equations of line $l$ and curve $C$;

(II) Ray $OM:\theta =\beta$ ($0 < \beta < \frac{\pi }{2}$) intersects curve $C$ at points $O$, $P$, and line $l$ at point $M$. Find the range of values for $\frac{\left| OP \right|}{\left| OM \right|}$.

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