
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 points A and B are respectively the left and right endpoints of the major axis of the ellipse $\frac{x^2}{36} + \frac{y^2}{20} = 1$, and point F is the right focus of the ellipse. Point P is on the ellipse and above the x-axis, with $PA \perpendicular PF$.
    (I) Find the coordinates of point P;
    (II) Let M be a point on the major axis AB of the ellipse, and the distance from M to the line AP is equal to $|MB|$, find the minimum distance from points on the ellipse to point M.

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