
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 the solution set of the system of linear inequalities in one variable $x$ is $\left\{\begin{array}{l}{\frac{x-4}{3}-x>2}\\{\frac{x-m}{2}\leq 0}\end{array}\right.$ is $x<-5$, and the solution of the fractional equation in variable $y$ $\frac{2-my}{3-y}+\frac{5}{y-3}=-3$ is an integer, then the sum of all integers $m$ that satisfy the conditions is ______.

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