
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 $xOy$, for a point M on the curve $C$, the ratio of the distance from M to the origin to the distance from M to the line $y = -p$ (where $p > 0$) is a constant $e$ (where $e > 0$). For the line $l$ with equation $\rho= \frac{4}{\cos\theta-2\sin\theta}$,
(I) Find the polar coordinate equation of curve $C$ and describe the shape of curve $C$;
(II) When $e=1$ and $p=1$, let M and N be two moving points on curve $C$ and line $l$, respectively. Find the minimum value of $|MN|$ and the coordinates of point M at that time.

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