
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 C: x²=4y with focus F, a line l passes through point P(-2, 2) and intersects the parabola C at points A and B.
(1) Find the equation of line AB when point P is the midpoint of AB.
(2) Find the minimum value of |AF|•|BF|.

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