
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 $x_1$ and $x_2$ are the two roots of the quadratic equation $x^2 - 5x - 3 = 0$, find:  
(1) $x_1^2 + x_2^2$  
(2) $\frac{1}{x_1} - \frac{1}{x_2}$.

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