
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 circle $C$ is the intersection point of the lines $x+y+1=0$ and $x-y-1=0$, and that the line $3x+4y-11=0$ intersects with circle $C$ at points $A$ and $B$ with $|AB|=6$, find the equation of circle $C$.

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