
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
The equation of the hyperbola $E_1: \frac{x^2}{4} - \frac{y^2}{5} = 1$ implies that $a^2 = 4$ and $b^2 = 5$. Therefore, the distance from the center to each foci of $E_1$ is $\sqrt{a^2+b^2} = \sqrt{9} = 3$. Since $E_2$ shares a common focus with $E_1$, we have that the distance from the center to each focus of $E_2$ is also equal to 3. Given that $a > b > 0$ for the ellipse $E_2: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, find the equation of this ellipse.

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