
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, 0, \( z_1 \), and \( z_2 \) form the vertices of a right triangle with \( z_2 \) being the vertex opposite the right angle. Find \( \frac{a^2}{b} \).

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