
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 \( f(x) \equiv x^{2} + p x + q = 0 \) are \( x_{1} \) and \( x_{2} \), which are numbers different from unity. What is the quadratic equation whose roots are

\[ y_{1} = \frac{x_{1} + 1}{x_{1} - 1} \quad \text{and} \quad y_{2} = \frac{x_{2} + 1}{x_{2} - 1} \quad? \]

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