
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 $x$, $\left\{{\begin{array}{l}{x-1≥2x+1}\\{2x-1＜a}\end{array}}\right.$, is $x\leqslant -2$, and the solution of the fractional equation in variable $y$, $\frac{{y-1}}{{y+1}}=\frac{a}{{y+1}}-2$, is negative, then the sum of all integers $a$ that satisfy the conditions is ______.

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