
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 defined by $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$ with $a > 0$ and $b > 0$, determine the range of the hyperbola's eccentricity if a line passing through its right focus and perpendicular to the $x$-axis intersects the hyperbola at points $A$ and $B$, and intersects the hyperbola's asymptotes at points $C$ and $D$, and $|AB| \geqslant \dfrac{3}{5} |CD|$.

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