
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
Given that $x\_1$ and $x\_2$ are the roots of the equation $x^{2}-2x-1=0$, find the value of the following algebraic expressions:

$(1) (x\_1+x\_2)(x\_1 \cdot x\_2)$;

$(2) (x\_1-x\_2)^{2}$.

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