
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
Let $z_1$ and $z_2$ be the complex roots of $z^2 + az + b = 0,$ where $a$ and $b$ are complex numbers. In the complex plane, the points 0, $z_1,$ and $z_2$ form an equilateral triangle. Let $z_2 = \omega z_1$ where $\omega = e^{2\pi i/3}$. Find $\frac{a^2}{b}$.

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