
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 inequality system about $x$ is $\left\{\begin{array}{l}{\frac{x-a}{2}＞0}\\{\frac{x-4}{3}+4＜x}\end{array}\right.$ is $x \gt 4$, and the fractional equation about $x$ $\frac{1-ax}{2-x}+\frac{3}{x-2}=1$ has an integer solution, then the sum of all integers $a$ that satisfy the conditions is ____.

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