
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 $M$ passes through two points $A(1,-1)$, $B(-1,1)$, and the center of the circle $M$ is on the line $x+y-2=0$.

(1) Find the equation of circle $M$.
(2) If $P(x,y)$ is on the circle $M$, find the range of values for $\frac{y+3}{x+3}$.

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