
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
For the polynomials \( f(x) = x^{2} + a x + b \) and \( g(y) = y^{2} + p y + q \) with roots \( x_{1}, x_{2} \) and \( y_{1}, y_{2} \) respectively, express their resultant in terms of \( a, b, p, q \):

$$
R(f, g) = \left( x_{1} - y_{1} \right) \left( x_{1} - y_{2} \right) \left( x_{2} - y_{1} \right) \left( x_{2} - y_{2} \right).
$$

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