
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 circle C with a radius of 2, whose center is on the positive x-axis, and the line $3x-4y+4=0$ is tangent to circle C.  
(I) Find the equation of circle C;  
(II) A line $l$ passing through point Q(0, -3) intersects circle C at two distinct points A($x_1$, $y_1$) and B($x_2$, $y_2$). If $\overrightarrow{OA} \cdot \overrightarrow{OB} = 3$ (O is the origin), find the equation of line $l$.

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