
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
Suppose a function $f(x)$ is an increasing function in a certain interval $I$ of its domain $D$, and $\frac{f(x)}{x}$ is a decreasing function in $I$. Then, $y=f(x)$ is called a "weakly increasing function" in $I$. Given that the function $g(x)=x^2+(4-m)x+m$ is a "weakly increasing function" in $(0, 2]$, find the value of the real number $m$.

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