
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 a hyperbola with equation $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, its asymptotes intersect with the line $x = \frac{a^2}{c}$ at points $A$ and $B$, and $F$ is the right focus of the hyperbola. If $\angle AFB$ is such that $60^\circ < \angle AFB < 90^\circ$, determine the range of values for the eccentricity of the hyperbola.

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