
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
In the Cartesian coordinate plane $(xOy)$, point $A(-2,0)$ is given. Point $B$ is on the circle $C$: $(x-2)^{2}+y^{2}=4$. Point $M$ is the midpoint of $AB$. If there exists a point $P$ on the line $l$: $y=kx-\sqrt{5}k$ such that $\angle OPM = 30^{\circ}$, find the range of values for the real number $k$.

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