
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/>$(1)$ Solve the system of inequalities $\left\{\begin{array}{l}\frac{2x-1}{3}-\frac{5x+1}{2}≤1\\ 5x-1＜3(x+1)\end{array}\right.$;<br/>$(2)$ Factorize $-b^{3}+4ab^{2}-4a^{2}b$;<br/>$(3)$ Solve the fractional equation $\frac{x}{x-1}-1=\frac{3}{(x-1)(x+2)}$;<br/>$(4)$ Simplify first, then evaluate $(1-\frac{{x}^{2}}{{x}^{2}+x})÷\frac{{x}^{2}-1}{{x}^{2}+2x+1}$, and choose one from $-1$, $0$, $1$, $2$ to substitute and evaluate.

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