
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 that $A$ is the right vertex of the hyperbola $C$: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$ ($a > 0$, $b > 0$), and a line parallel to the $y$-axis passing through the left focus $F$ intersects the hyperbola $C$ at points $P$ and $Q$. If $\triangle APQ$ is an acute triangle, then the range of the eccentricity of the hyperbola $C$ is \_\_\_\_\_\_.

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