
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 an ellipse with the equation $\frac{y^{2}}{a^{2}} + \frac{x^{2}}{b^{2}} = 1 (a > b > 0)$ that has an eccentricity of $\frac{\sqrt{3}}{2}$ and a minor axis length of 4. The ellipse intersects the line $y = x + 2$ at points A and B.

(1) Find the equation of the ellipse.
(2) Find the length of chord $|AB|$.

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