
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 \( d, e, f, g \) be the roots of \( x^4 + rx^2 + sx + t = 0 \). Compute the determinant
\[
\begin{vmatrix}
d & e & f & g \\
e & f & g & d \\
f & g & d & e \\
g & d & e & f
\end{vmatrix}.
\]

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