
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 $g : \mathbb{C} \to \mathbb{C}$ be defined by $g(z) = z^2 - iz + 2$. Determine how many complex numbers $z$ exist such that $\text{Im}(z) < 0$ and both the real and the imaginary parts of $g(z)$ are integers with absolute values at most $5$.

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