
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 first, then find the value: $\frac{2}{{{x^2}+x}}\div (1-\frac{{x-1}}{{{x^2}-1}}$), where $x$ is an integer solution of the inequality system $\left\{{\begin{array}{l}{2(x-1)<x+1}\\{5x+3\geq 2x}\end{array}}\right.$.

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