
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 $x=2$. The curve $C$ is given by the parametric equations $\begin{cases} x = \cos \alpha \\ y = 1+\sin \alpha \end{cases}$ (where $\alpha$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis.
1. Find the polar equations of line $l$ and curve $C$.
2. Ray $OM$: $\theta=\beta$ (where $0 < \beta < \frac{\pi}{2}$) intersects curve $C$ at points $O$ and $P$, and intersects line $l$ at point $M$. Find the range of values for $\frac{|OP|}{|OM|}$.

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