
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 a complex number $z=2+xi$ (where $i$ is the imaginary unit) and $\overline{z}•(1-i)$ is a purely imaginary number ($\overline{z}$ is the conjugate of $z$). Find:<br/>
$(1)$ The value of the real number $x$ and the modulus of the complex number $z$;<br/>
$(2)$ If the complex number ${z_1}=\frac{{m+{i^3}}}{z}$ corresponds to a point in the fourth quadrant of the complex plane, find the range of values for the real number $m$.

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