
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 moving point P(x, y) on curve C, which satisfies that its distance to point F(0, 1) is 1 less than its distance to the line l: y = -2.
(Ⅰ) Find the equation of curve C;
(Ⅱ) A moving point E is on line l, and tangents EA, EB to curve C are drawn from point E, with A and B being the points of tangency. Does line AB always pass through a fixed point? If so, find the coordinates of the fixed point; if not, please explain why.

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