
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 that $z$ is a complex number, $\overline{z}-4$ is a pure imaginary number, and $\frac{z}{{2-i}}$ is a real number.  
$(1)$ Find the complex number $z$;  
$(2)$ If the point corresponding to the complex number $\left(z+ai\right)^{2}$ on the complex plane is located in the second quadrant, find the range of real number $a$.

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