
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
The solution set of the one-variable linear inequality system about $x$ is $\left\{{\begin{array}{l}{m-\frac{3}{2}x≥-1-x}\\{4-x≥0}\end{array}}\right.$. The solution set is $x≤4$. For the fractional equation about $y$, $\frac{{my}}{{y-2}}+1=\frac{{-3y}}{{2-y}}$ has an integer solution. Find the product of all integers $m$ that satisfy the conditions.

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