
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
The equation of the circle with center at point $\left(1,-1\right)$ and tangent to the line $x-y+2=0$ is $(x-1)^{2}+\left(y+1\right)^{2}=r^{2}$, where $r$ is the distance from the center to the tangent line. Find the value of $r^{2}$.

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