
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 on the plane, establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given that the polar coordinates of two points $M$ and $N$ on the line $l$ are $(2,0)$ and $(\frac{2\sqrt{3}}{3}, \frac{\pi}{2})$, respectively, and the parametric equations of circle $C$ are $x=2+2\cos\theta$ and $y=\sqrt{3}+2\sin\theta$ ($\theta$ is the parameter).
(I) Let $P$ be the midpoint of segment $MN$. Find the rectangular equation of line $OP$.
(II) Determine the relationship between line $l$ and circle $C$.

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