
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 parametric equations of curve C as $\begin{cases} x=-1+2\cos\theta \\ y=1+2\sin\theta \end{cases}$ (where $\theta$ is the parameter), with the origin O as the pole and the non-negative half of the x-axis as the polar axis, establish the polar coordinate equation.

1. Find the polar coordinate equation of curve C.
2. If line $l$ defined by $\theta=\alpha$ ($\alpha \in [0,\pi)$, $\rho \in \mathbb{R}$) 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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