
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
Let $\alpha$ and $\beta$ be the roots of the equation

$$
x^{2}+p x+q=0
$$

and $\gamma$ and $\delta$ be the roots of the equation

$$
x^{2}+P x+Q=0
$$

Express the product

$$
(\alpha-\gamma)(\beta-\gamma)(\alpha-\delta)(\beta-\delta)
$$

in terms of the coefficients of the given equations.

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