Let $p,$ $q,$ $r,$ $s$ be the roots of
\[3x^4 - x + 12 = 0.\]Find $pqr + pqs + prs + qrs.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $p,$ $q,$ $r,$ $s$ be the roots of
\[3x^4 - x + 12 = 0.\]Find $pqr + pqs + prs + qrs.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{3}
Let $p,$ $q,$ $r,$ $s$ be the roots of
\[3x^4 - x + 12 = 0.\]Find $pqr + pqs + prs + qrs.$
train