
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 equation \(x^{2} + p x + q = 0\) has roots \(x_{1}\) and \(x_{2}\). Write the equation whose roots will be the numbers \(y_{1}, y_{2}\) equal to:
a) \(x_{1}^{3}\), \(x_{2}^{3}\);
b) \(\frac{1}{x_{1}^{2}}, \frac{1}{x_{2}^{2}}\);
c) \(x_{1}+\frac{1}{x_{2}}, x_{2}+\frac{1}{x_{1}}\);
d) \(\frac{x_{2}}{x_{1}}, \frac{x_{1}}{x_{2}}\).

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