
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 $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a>0,b>0)$, if the distance from one of its foci, $F$, to one of its asymptotes is greater than the length of the real axis, what is the range of values for the eccentricity of the hyperbola?

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