
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
Let the ellipse \(\Gamma: \frac{x^{2}}{a^{2}} + y^{2} = 1\) (where \(a > 1\)) be given. Any circle centered at \(A(0,1)\) intersects the ellipse \(\Gamma\) at most three points. Determine the range of the eccentricity of the ellipse.

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