
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 point A(1, -1) on circle M is symmetric about the line $y=x$ and still lies on circle M, and the line $x+y-1=0$ intersects circle M at a chord with length $\sqrt{14}$.  
(1) Find the equation of circle M;  
(2) Let P be a moving point on the line $x+y+2=0$, and PE, PF are two tangents from P to circle M, with E and F being the points of tangency. Find the minimum area of quadrilateral PEMF.

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