Let $a,$ $b,$ $c,$ $d$ be positive real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[\frac{a}{b + c + d} + \frac{b}{a + c + d} + \frac{c}{a + b + d} + \frac{d}{a + b + c}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c,$ $d$ be positive real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[\frac{a}{b + c + d} + \frac{b}{a + c + d} + \frac{c}{a + b + d} + \frac{d}{a + b + c}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{4}{3}
Let $a,$ $b,$ $c,$ $d$ be positive real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[\frac{a}{b + c + d} + \frac{b}{a + c + d} + \frac{c}{a + b + d} + \frac{d}{a + b + c}.\]
train