
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 $\left\{{\begin{array}{l}{x+1≤\frac{{2x-5}}{3}}\\{a-x＞1}\end{array}}\right.$ is $x\leqslant -8$, and the solution of the fractional equation about $y$ is $4+\frac{y}{{y-3}}=\frac{{a-1}}{{3-y}}$ is a non-negative integer, then the sum of all integers $a$ that satisfy the conditions is ____.

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