Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
Let $0 \le a \le 1$ and $0 \le b \le 1.$  Find the largest possible value of
\[\frac{a + b}{ab + 1}.\]
train