
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 $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ ($a > 1, b > 0$) with a focal length of $2c$, and a line $l$ passing through points $(a,0)$ and $(0,b)$, and the sum of the distances from point $(1,0)$ to line $l$ and from point $(-1,0)$ to line $l$ is $s \geq \dfrac{4}{5}c$. Find the range of the eccentricity $e$ of the hyperbola.

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