
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
A point M with coordinates $(\sqrt{3}, y_0)$ is given. A circle O with equation $x^2 + y^2 = 1$ is also given. Draw a tangent line from point M to circle O, and denote the tangent point as N. If $\angle OMN \geq \frac{\pi}{6}$, determine the range of $y_0$.

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