
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 circle O: x²+y²=r² (r>0) passes through point A (0,5), and intersects the positive semi-axis of the x-axis at point B.
(I) r=____; (fill in the answer directly in the corresponding space on the answer card)
(II) Does there exist a point P on circle O such that the area of ΔPAB is 15? If so, find the coordinates of point P; if not, explain the reason.

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