
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 \(x\), \(y\), and \(z\) be the roots of the cubic equation \(x^3 + sx^2 + tx = 0\). Compute the determinant:
\[
\begin{vmatrix}
x & y & z \\
y & z & x \\
z & x & y
\end{vmatrix}.
\]

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