
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: $\left\{\begin{array}{l}{x-4＜2(x-1)…①}\\{\frac{1+2x}{3}≥x…②}\end{array}\right.$;<br/>$(2)$ Solve the equation: $\frac{x-2}{x-3}=2-\frac{1}{3-x}$;<br/>$(3)$ Simplify first, then find the value: $(1-\frac{1}{x+2})÷\frac{x^2-1}{x+2}$, where $x=3$.

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