
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 a circle with equation $x^2 + y^2 - 4x - 4y - 10 = 0$, there are at least three distinct points on the circle whose distances to the line $l : ax + by = 0$ are $2\sqrt{2}$. Determine the range of possible values for the angle of inclination of line $l$.

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