
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 $l$: $y=- \frac {1}{2}x+b$ intersects the parabola at points $A$ and $B$.
(I) If the $x$-axis is tangent to the circle with $AB$ as its diameter, find the equation of the circle;
(II) If the line $l$ intersects the negative semi-axis of $y$, find the maximum area of $\triangle AOB$.

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