
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 $a,$ $b,$ $c,$ $d$ be the roots of the equation $x^4 + px^2 + qx + r = 0.$ Compute the determinant
\[
\begin{vmatrix}
a & b & c & d \\
b & c & d & a \\
c & d & a & b \\
d & a & b & c
\end{vmatrix}.
\]

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