
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
A complex number $z$ is given, where $z+2i$ and $\frac{z}{2-i}$ are both real numbers (here $i$ is the imaginary unit). Also, the point corresponding to the complex number $(z+ai)^{2}$ lies in the first quadrant of the complex plane. Determine the range of the real number $a$.

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