If $\mathbf{a}$ and $\mathbf{b}$ are vectors such that $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 14$, then find the smallest possible value of $\|\mathbf{a} + \mathbf{b}\|$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\mathbf{a}$ and $\mathbf{b}$ are vectors such that $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 14$, then find the smallest possible value of $\|\mathbf{a} + \mathbf{b}\|$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
11
If $\mathbf{a}$ and $\mathbf{b}$ are vectors such that $\|\mathbf{a}\| = 3$ and $\|\mathbf{b}\| = 14$, then find the smallest possible value of $\|\mathbf{a} + \mathbf{b}\|$.
train