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

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