
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 the circle $x^2 + y^2 = 16$, and the line $l: y = x + b$. If there are at least three points on the circle such that the distance from these points to the line $l$ is equal to 1, what is the range of values for $b$?

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