
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 the hyperbola $x^{2}-\frac{y^2}{m^2}=1\left(m \gt 0\right)$, whose asymptotes are $y=\pm mx$, and the circle $x^{2}+\left(y+2\right)^{2}=1$ with center at $\left(0,-2\right)$ and radius $1$, if the asymptotes of the hyperbola and the circle do not intersect, then the range of values for the focal length of the hyperbola is ____.

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