
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
If a linear function is $y=(4-m)x-3$, where $y$ increases as $x$ increases, and the fractional equation about $z$ is $\frac{m}{z-1}-2=\frac{3}{1-z}$ has a positive integer solution, then the sum of all integer values of $m$ that satisfy the condition is ______.

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