Let \( ABC \) be a triangle such that \( \overrightarrow{BC}=\vec{a} \), \( \overrightarrow{CA}=\vec{b} \), \( \overrightarrow{AB}=\vec{c} \), \( |\vec{a}|=6\sqrt{2} \), \( |\vec{b}|=2\sqrt{3} \) and \( \vec{b}\cdot\vec{c}=12 \). Consider the statements:
(S1): \( \big|(\vec{a}\times\vec{b})+(\vec{c}\times\vec{b})\big| - |\vec{c}| = 6(2\sqrt{2}-1) \)
(S2): \( \angle ACB = \cos^{-1}\!\left(\sqrt{\dfrac{2}{3}}\right) \)
Then
