
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
$(1)$ Calculate: ${(-3{x}^{2}{y}^{-3})}^{-2}•{(-2{x}^{2}y)}^{3}÷(-\frac{1}{6}x{y}^{2})$.  
$(2)$ Simplify first: $(\frac{4}{x-2}+x+2)÷\frac{{x}^{2}-2x}{{x}^{2}-4x+4}$, then choose a suitable number from $0$, $1$, $2$, $3$ to substitute and evaluate.

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