
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 ellipse \\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 (a > b > 0)\\), where \\(F_1\\) and \\(F_2\\) are the left and right foci of the ellipse, and \\(l\\) is the right directrix. If there exists a point \\(P\\) on the ellipse such that the distance from \\(P\\) to \\(F_1\\) is twice the distance from \\(P\\) to the line \\(l\\), then the range of the eccentricity of the ellipse is.

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