
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
It is known that circle C passes through the point Q(1, 1) and is symmetric to circle M with respect to the line 2x + y + 2 = 0, where circle M is given by $(x+2)^2 + (y+2)^2 = r^2$ (r > 0).
(1) Find the equation for circle C.
(2) Let P be a moving point on the line 3x + 4y + 8 = 0, and let PA and PB be two tangents to circle C with A and B as the tangent points. Find the minimum value of the area of quadrilateral PABC.

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