
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 the parabola $y^2=2px$ ($p>0$), the distance from the focus to the directrix is 4, and a line passing through point P(1, -1) intersects the parabola at points A and B.  
(Ⅰ) Find the equation of the parabola;  
(Ⅱ) If point P is exactly the midpoint of line segment AB, find the equation of line AB.

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