Let $a,$ $b,$ $c,$ $d$ be nonnegative real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[a^2 + b^2 + c^2 + d^2.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c,$ $d$ be nonnegative real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[a^2 + b^2 + c^2 + d^2.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{4}
Let $a,$ $b,$ $c,$ $d$ be nonnegative real numbers such that $a + b + c + d = 1.$  Find the minimum value of
\[a^2 + b^2 + c^2 + d^2.\]
train