
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
The roots of the equation \( x^{2}+px+q \) are \( x_{1} \) and \( x_{2} \). Calculate the following expressions:

\[ \frac{1}{x_{1}}+\frac{1}{x_{2}}, \quad \frac{1}{x_{1}^{2}}+\frac{1}{x_{2}^{2}}, \quad \frac{1}{x_{1}^{3}}+\frac{1}{x_{2}^{3}} \]

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