
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
Calculate:<br/>$(1)$ Simplify $\frac{{x-1}}{x}÷\frac{{2x-2}}{{{x^2}}}$;<br/>$(2)$ Simplify first, then evaluate $(2-\frac{{a-1}}{{a+1}})÷\frac{{{a^2}+6a+9}}{{a+1}}$, where $a=2$.

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