
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
The hyperbola $\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ (where $a > 1$ and $b > 0$) has a focal distance of $2c$. A straight line l passes 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 $s \geq \frac {4}{5}c$. Find the range of possible values for the eccentricity $e$ of the hyperbola.

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