
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, with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinates of two points $M$ and $N$ on the line $l$ are $(3,π)$ and $(√3, \frac{π}{2})$, respectively.
(I) Let $P$ be a moving point on the line segment $MN$. Find the rectangular coordinates of point $P$ when the line segment $OP$ takes the minimum value.
(II) Find the parametric equation of the circle $C$ with $MN$ as its diameter, and then find the length of the chord obtained when the line $OP$ intersects with the circle $C$ under the condition of (I).

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