
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 $C:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ with its right focus $F$, one of its asymptotes intersects the circle $(x-c)^{2}+y^{2}=a^{2} \, (c^{2}=a^{2}+b^{2}, c > 0)$ at points $A$ and $B$. If $\triangle{ABF}$ is an acute triangle, determine the range of the eccentricity of hyperbola $C$.

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