
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
Consider the hyperbola given by the equation $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ ($a > 0, b > 0$). If a line with slope $l$ passing through the right focus $F$ of the hyperbola intersects both branches, and when the slope is $3$, the line intersects only the right branch at two distinct points, determine the range of values for the eccentricity of the hyperbola.

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