
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
Consider all possible pairs of quadratic equations $x^{2}+px+q=0$ and $x^{2}+qx+p=0$ such that each equation has two distinct roots. Is it true that the expression $\frac{1}{x_{1} x_{3}}+\frac{1}{x_{1} x_{4}}+\frac{1}{x_{2} x_{3}}+\frac{1}{x_{2} x_{4}}$, where $x_{1}, x_{2}$ are the roots of the first equation, and $x_{3}, x_{4}$ are the roots of the second equation, is the same for all such pairs (i.e., it does not depend on the values of $p$ and $q$)? Justify your answer.

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