
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
The solution to the fractional equation about $x$, $\frac{{3x-a}}{{x-3}}+\frac{{x+1}}{{3-x}}=1$, is a positive number. The solution set of the inequality system about $y$, $\left\{\begin{array}{l}{y+9≤2(y+2)}\\{\frac{{2y-a}}{3}＞1}\end{array}\right.$, is $y\geqslant 5$. Find the sum of all integers $a$ that satisfy the conditions.

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