
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
For the quadratic function of $x$, $y=(a-2)x^2+5x-\frac{5}{4}$ has intersection points with the $x$-axis. If the solution of the fractional equation about $y$, $\frac{ay-3}{y-2}+1=\frac{3y-1}{2-y}$, is an integer, then the sum of all integer values of $a$ that satisfy the condition is ______.

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