
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 radius 2, whose center is on the positive x-axis, the line $3x-4y+4=0$ is tangent to the circle.
(1) Find the equation of circle C;
(2) Given point Q(0, 3), let P be a moving point on circle C, and find the equation of the trajectory of the midpoint M of segment PQ;
(3) A line l passing through point Q(0, -3) intersects circle C at two distinct points A$(x_1, y_1)$ and B$(x_2, y_2)$, and $x_1x_2+y_1y_2 = 3$. Find the area of triangle ABC.

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