
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
Solve the following questions:

$(1)$ Solve the system of inequalities: $\left\{\begin{array}{l}{3x+6≥5(x-2)①}\\{\frac{x-5}{2}-\frac{4x-3}{3}＜1②}\end{array}\right.$.

$(2)$ Simplify first, then find the value: $(1-\frac{2}{x-1})÷\frac{x^2-6x+9}{x-1}$. Try substituting one of the numbers $0$, $1$, $2$, $3$ of your choice to find the value.

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