Let $\mathbf{a}$ and $\mathbf{b}$ be two non-zero vectors such that
\[\mathbf{a} \times (\mathbf{a} \times \mathbf{b}) = -3 \mathbf{b}.\]Find $\|\mathbf{a}\|.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{a}$ and $\mathbf{b}$ be two non-zero vectors such that
\[\mathbf{a} \times (\mathbf{a} \times \mathbf{b}) = -3 \mathbf{b}.\]Find $\|\mathbf{a}\|.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{3}
Let $\mathbf{a}$ and $\mathbf{b}$ be two non-zero vectors such that
\[\mathbf{a} \times (\mathbf{a} \times \mathbf{b}) = -3 \mathbf{b}.\]Find $\|\mathbf{a}\|.$
train