
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: $\left\{\begin{array}{l}{2x-1＜5,①}\\{\frac{4-x}{2}≥1,②}\end{array}\right.$<br/>$(2)$ Simplify first, then find the value: $\frac{1}{a-1}÷(\frac{{a}^{2}+a}{{a}^{2}-1}+\frac{1}{a-1})$, where $a=(-2023)^0+(\frac{1}{2})^{-1}⋅$

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