
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 there is a solution to the system of linear inequalities in one variable $x$: $\left\{\begin{array}{l}{x+1>\frac{x-1}{3}}\\{x+a<3}\end{array}\right.$, and the solution to the fractional equation in variable $y$: $\frac{{y-a}}{{y-2}}+1=\frac{1}{{y-2}}$ is a positive integer, then the sum of all integer values of $a$ that satisfy the conditions is ____.

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