
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
Simplify and find the value of $(\frac{3}{{x-1}}-x-1)÷\frac{{x-2}}{{x-1}}$, where $x$ is an integer solution of the inequality system $\left\{{\begin{array}{l}{x-3(x-2)≥2}\\{4x-2＜5x-1}\end{array}}\right.$.

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