
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
$(1)$ Solve the system of inequalities $\left\{\begin{array}{c}10-3x＜-5\\ \frac{x}{3}≥4-\frac{x-2}{2}\end{array}\right.$; <br/>$(2)$ Simplify: $\frac{2}{a+1}-\frac{a-2}{{a}^{2}-1}÷\frac{a(a-2)}{{a}^{2}-2a+1}$.

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