
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
A circle with its center at point $(1, 1)$ has a radius $\sqrt{r}$. A line given by the equation $x + y = r$ is tangent to this circle. If $r$ is positive, find the value of $r$.
A) \(3 - \sqrt{5}\)  
B) \(3\)  
C) \(2\sqrt{5}\)  
D) \(3 + \sqrt{5}\)  
E) \(5\)

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