
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 there are at least three distinct points on the circle $x^{2}+y^{2}-4x-4y-10=0$ that are $2 \sqrt {2}$ units away from the line $l$: $y=x+b$, find the range of values for $b$.

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