
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 two 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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