
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 equation of the parabola is $y^2 = 4x$, and $O$ is the origin of the coordinates:
(Ⅰ) Points $A$ and $B$ are two points on the parabola, and $P(3, 2)$ is the midpoint of line segment $AB$. Determine the equation of line $AB$.
(Ⅱ) A line $l$ passing through the point $(2, 0)$ intersects the parabola at points $M$ and $N$. If the area of $\triangle OMN$ is $6$, find the equation of line $l$.

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