
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
Ellipse \( C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) where \( a > b > 0 \), has left and right foci \( F_{1} \) and \( F_{2} \) respectively. If there are exactly 6 distinct points \( P \) on the ellipse such that \( \triangle F_{1} F_{2} P \) is an isosceles triangle, determine the range of the eccentricity of the ellipse \( C \).

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