Determine the sum of the $y$-coordinates of the four points of intersection of $y  = x^4 - 5x^2 - x + 4$ and $y = x^2 - 3x.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Determine the sum of the $y$-coordinates of the four points of intersection of $y  = x^4 - 5x^2 - x + 4$ and $y = x^2 - 3x.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
Determine the sum of the $y$-coordinates of the four points of intersection of $y  = x^4 - 5x^2 - x + 4$ and $y = x^2 - 3x.$
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