
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 that the eccentricity of the ellipse $C:\frac{x^{2}}{2}+y^{2}=1$ is equal to the slope of one asymptote of the hyperbola $E: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\left(a > 0,b > 0\right)$, find the eccentricity of the hyperbola $E$.

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