Consider vectors \(\mathbf{u} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\) and \(\mathbf{v} = \begin{pmatrix} 6 \\ 8 \end{pmatrix}\). Determine the cosine of the angle between \(\mathbf{u}\) and \(\mathbf{v}\). Let's think step by step and output the final answer within \boxed{}.
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