Let $a,$ $b,$ $c$ be real numbers such that $a + b + c = 0.$  Find the set of all possible values of $ab + ac + bc.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c$ be real numbers such that $a + b + c = 0.$  Find the set of all possible values of $ab + ac + bc.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,0]
Let $a,$ $b,$ $c$ be real numbers such that $a + b + c = 0.$  Find the set of all possible values of $ab + ac + bc.$
train