
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 that the center of the circle lies on the line $x+y-1=0$, and points $A(-1,4)$ and $B(1,2)$ are two points on the circle.  
$(1)$ Find the equation of the circle.  
$(2)$ If point $P$ is a moving point on the circle and $O$ is the origin, find the range of slopes of the line $OP$.

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