Let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that
\[\mathbf{v} = \operatorname{proj}_{\mathbf{a}} \mathbf{v} + \operatorname{proj}_{\mathbf{b}} \mathbf{v}\]for all vectors $\mathbf{v}.$  Enter all possible values of $\mathbf{a} \cdot \mathbf{b},$ separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that
\[\mathbf{v} = \operatorname{proj}_{\mathbf{a}} \mathbf{v} + \operatorname{proj}_{\mathbf{b}} \mathbf{v}\]for all vectors $\mathbf{v}.$  Enter all possible values of $\mathbf{a} \cdot \mathbf{b},$ separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
0
Let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that
\[\mathbf{v} = \operatorname{proj}_{\mathbf{a}} \mathbf{v} + \operatorname{proj}_{\mathbf{b}} \mathbf{v}\]for all vectors $\mathbf{v}.$  Enter all possible values of $\mathbf{a} \cdot \mathbf{b},$ separated by commas.
train