
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 $u$ and $v$ be the roots of the equation $x^2 + rx + 1 = 0$, and let $s$ and $t$ be the roots of $x^2 + sx + 1 = 0$. Express
\[(u - s)(v - s)(u + t)(v + t)\] in terms of $r$ and $s$.

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