
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 $y^{2}=4x$ and the line $l: x+2y-2b=0$ intersecting the parabola at points $A$ and $B$.

(Ⅰ) If the circle with diameter $AB$ is tangent to the $x$-axis, find the equation of the circle;

(Ⅱ) If the line $l$ intersects the negative half of the $y$-axis, find the maximum area of $\triangle AOB$ ($O$ is the origin).

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