
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 $z=\frac{{6-4mi}}{{1+i}}$ ($m\in R$, $i$ is the imaginary unit).<br/>$(1)$ If $z$ is a real number, find the value of the real number $m$;<br/>$(2)$ Let $\overline{z}$ be the conjugate of $z$, and the complex number $\overline{z}-4z$ corresponds to a point in the first quadrant of the complex plane. Find the range of real number $m$.

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