
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
The distance from point P to the line $y=-3$ is 2 units greater than its distance to point F $(0, 1)$.
(Ⅰ) Find the equation of the trajectory C of point P.
(Ⅱ) Let point A be $(-4, 4)$, and a line $l$ passing through point B $(4, 5)$ intersects the trajectory C at points M and N. The slopes of lines AM and AN are $k_1$ and $k_2$ respectively. Find the minimum value of $|k_1 - k_2|$.

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