
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
Given the parameterized equations of curve $C$ as $x=-1+2\cos \theta, y=1+2\sin \theta$, where $\theta$ is the parameter, establish its polar coordinate equation with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis.
(1) Find the polar coordinate equation of curve $C$;
(2) If line $l$: $\theta=\alpha (\alpha \in [0,\pi))$, $\rho \in \mathbb{R}$ intersects curve $C$ at points $A$ and $B$, and $M$ is the midpoint of segment $AB$, find the maximum value of $|OM|$.

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