
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: $A=({\frac{{3x}}{{x-1}}-\frac{x}{{x+1}}})÷\frac{x}{{{x^2}-1}}$, simplify $A$ first, then choose a suitable value from the solution set of the inequality system $\left\{\begin{array}{l}{x-3(x-2)≥2①}\\{4x-2＜5x-1②}\end{array}\right.$ to substitute in, and find the value of $A$.

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