
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
Calculate:<br/>$(1)$ Factorize: $x^{2}(3m-2n)+y^{2}(2n-3m)$;<br/>$(2)$ Solve the inequality system: $\left\{\begin{array}{l}{\frac{x-3}{2}+3>x+1}\\{1-3(x-1)<8-x}\end{array}\right.$;<br/>$(3)\frac{3-x}{x-4}+\frac{1}{4-x}=1$;<br/>$(4)(\frac{2}{a+1}+\frac{a+2}{{a}^{2}-1})÷\frac{a}{a-1}$, where $a=3$.

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