
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 $O: x^2 + y^2 = 1$, a point $P$ on the line $l: x + y + k = 0$ draws two tangents to circle $O$, with the points of tangency being $A$ and $B$. If there exists at least one point $P$ on line $l$ such that $\angle APB = 60^\circ$, then the range of values for $k$ is \_\_\_\_\_\_.

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