
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 parabola $C_{1}:y^{2}=8x$ with focus $F$, and an ellipse $C_{2}:\dfrac{x^{2}}{m^{2}}+\dfrac{y^{2}}{n^{2}}=1(m > n > 0)$ whose one focus coincides with the focus of the parabola $C_{1}$. If there exist two distinct points on the ellipse $C_{2}$ that are symmetric with respect to the line $l:y=\dfrac{1}{4}x+\dfrac{1}{3}$, then the range of the eccentricity $e$ of the ellipse $C_{2}$ is \_\_\_\_.

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