
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
$(1)$ Given $x=1-\sqrt{3}$ and $y=1+\sqrt{3}$, find the value of $x^{2}+y^{2}-xy-2x+2y$. <br/>$(2)$ Simplify first, then find the value of $\frac{1-2a+{a}^{2}}{a-1}-\frac{\sqrt{{a}^{2}-2a+1}}{{a}^{2}-a}$, where $a=\frac{1}{2-\sqrt{3}}$.

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