
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
1. Find the real number $m$ such that the eccentricity of the hyperbola $\frac{{x}^{2}}{m}+\frac{{y}^{2}}{2}=1$ is equal to $2$.
2. Given that the length of the major axis of an ellipse is twice the length of the minor axis, and the ellipse passes through the point $(2,-6)$, find the equation of the ellipse.

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