
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 the ellipse $E: \dfrac{y^2}{a^2} + \dfrac{x^2}{b^2} = 1 \,(a > b > 0)$ that passes through the points $A(\sqrt{5}, 0)$ and $B(0, 3)$, calculate the eccentricity of ellipse $E$.

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