
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
A circle M passes through two points A(1, -1) and B(-1, 1), and the center M is on the line x + y - 2 = 0.
(1) Find the standard equation of circle M.
(2) Let P be a moving point on the line 3x + 4y + 8 = 0, and PA, PB are the two tangents of circle M with A and B as the points of tangency. Find the minimum value of the area of the quadrilateral PAMB.

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