
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
Given the equation $\frac{ax}{x-2}=\frac{3+a}{x-2}-\frac{x}{2-x}$ concerning $x$, for the solution to be an integer, determine the number of non-negative values of $a$ such that the inequality system $\begin{cases} & 2x-3 > 9 \\\\ & x-a < 0 \\\\ \end{cases}$ has no solution.

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