
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 \(C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a>b>0)\) with the left and right foci as \(F_{1}\) and \(F_{2}\) respectively, where the focal distance is \(2c\). The point \(N\left(\frac{3c}{2}, \frac{\sqrt{2}c}{2}\right)\) is inside the ellipse, and the point \(M\) is a moving point on the ellipse \(C\). It is given that the condition \(\left|M F_{1}\right|+|M N|<2 \sqrt{3}\left|F_{1} F_{2}\right|\) always holds. Determine the range of the eccentricity of the ellipse \(C\).

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