
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
A circle C passes through the point (0, -1) with its center on the positive y-axis, and it is externally tangent to the circle whose equation is \((x-4)^2+(y-4)^2=9\).
(Ⅰ) Find the equation of circle C;
(Ⅱ) A line l passes through the point (0, 2) and intersects circle C at points A and B. If the origin point O is inside the circle whose diameter is AB, determine the range of possible values for the slope angle α of line l.

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