
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/>$(1)(\sqrt{48}-\frac{1}{4}\sqrt{6})\div (-\frac{1}{9}\sqrt{27})$;<br/>$(2)$ Given $x=\frac{1}{2}(\sqrt{3}+1)$, $y=\frac{1}{2}(1-\sqrt{3})$, find the value of $x^{2}+y^{2}-2xy$.

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