
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, taking the origin O as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. It is known that two points M and N on line $l$ have polar coordinates $(2,0)$ and $\left(\frac{2\sqrt{3}}{3}, \frac{\pi}{2}\right)$, respectively. The circle C has the parametric equations $\begin{cases} x=2+2\cos\theta \\ y=\sqrt{3}+2\sin\theta \end{cases}$ (where $\theta$ is the parameter).
- (I) Let P be the midpoint of segment MN. Find the equation of line OP in Cartesian coordinates.
- (II) Determine the positional relationship between line $l$ and circle C.

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