
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 parabola $C$ with its vertex at the origin and the equation of the directrix as $x=-1$  
(Ⅰ) Find the equation of the parabola $C$.  
(Ⅱ) If a line passes through the focus of the parabola $C$ and intersects the parabola at points $A$ and $B$, and the x-coordinate of the midpoint of segment $AB$ is 2, find the equation of line $AB$.

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