
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 the system of inequalities $\left\{\begin{array}{l}\frac{x-2}{4}＜\frac{x-1}{3}\\ 3x-m≤3-x\end{array}\right.$ has exactly 2 integer solutions, and the system of equations $\left\{\begin{array}{l}mx+y=4\\ 3x-y=0\end{array}\right.$ also has integer solutions, find the sum of all integers m that satisfy the conditions.

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