
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 circles $C\_1$: $x^{2}+2cx+y^{2}=0$ and $C\_2$: $x^{2}-2cx+y^{2}=0$, where $c$ is the semi-latus rectum of the ellipse $C$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. If both circles $C\_1$ and $C\_2$ are inside the ellipse, determine the range of the eccentricity of the ellipse.

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