
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 evaluate the expression: $$\frac{x}{x-1} \div \frac{x^2-x}{x^2-2x+1} - \frac{x+2}{x+1}$$, where $x$ is an integer solution to the system of inequalities: $$\begin{cases} 3x + 7 > 1 \\ 2x - 1 < 5 \end{cases}$$

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