Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|2\vec{a} + 3\vec{b}| = |3\vec{a} + \vec{b}|$ and the angle between $\vec{a}$ and $\vec{b}$ is $60^\circ$. If $\frac{1}{8}\vec{a}$ is a unit vector, then $|\vec{b}|$ is equal to:
\( 8 \)
\( 5 \)
\( 4 \)
\( 6 \)
