The roots of $x^4 - Kx^3 + Kx^2 + Lx + M = 0$ are $a,$ $b,$ $c,$ and $d.$   If $K,$ $L,$ and $M$ are real numbers, compute the minimum value of the sum $a^2 + b^2 + c^2 + d^2.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The roots of $x^4 - Kx^3 + Kx^2 + Lx + M = 0$ are $a,$ $b,$ $c,$ and $d.$   If $K,$ $L,$ and $M$ are real numbers, compute the minimum value of the sum $a^2 + b^2 + c^2 + d^2.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
The roots of $x^4 - Kx^3 + Kx^2 + Lx + M = 0$ are $a,$ $b,$ $c,$ and $d.$   If $K,$ $L,$ and $M$ are real numbers, compute the minimum value of the sum $a^2 + b^2 + c^2 + d^2.$
train