
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 a circle C that passes through point A(0, 2) and point B(2, -2), and the center of circle C lies on the line x - y + 1 = 0.
(Ⅰ) Find the standard equation of circle C
(Ⅱ) If a line with slope m passes through point (1, 4) and the chord intercepted by circle C has a length of 6, find the slope-intercept equation of line m.

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