
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 sum of the maximum integer solution and the minimum integer solution of the inequality system about $x$ $\left\{\begin{array}{l}{\frac{x-10}{5}≤-1-\frac{1}{5}x}\\{x-1＞-\frac{1}{2}m}\end{array}\right.$ is $-2$, then the sum of the integers $m$ that satisfy the condition is ______.

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