Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-8
Let $a,$ $b,$ $c$ be the roots of $x^3 - 7x + 2 = 0.$  Find
\[abc + ab + ac + bc + a + b + c + 1.\]
train