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 $\|\mathbf{a}\|.$The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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