Let $a_1,$ $a_2,$ $\dots,$ $a_{12}$ be real numbers such that $a_1 + a_2 + \dots + a_{12} = 1.$  Find the minimum value of
\[a_1^2 + a_2^2 + \dots + a_{12}^2.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a_1,$ $a_2,$ $\dots,$ $a_{12}$ be real numbers such that $a_1 + a_2 + \dots + a_{12} = 1.$  Find the minimum value of
\[a_1^2 + a_2^2 + \dots + a_{12}^2.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{12}
Let $a_1,$ $a_2,$ $\dots,$ $a_{12}$ be real numbers such that $a_1 + a_2 + \dots + a_{12} = 1.$  Find the minimum value of
\[a_1^2 + a_2^2 + \dots + a_{12}^2.\]
train