Let \( \vec a=2\hat i-\hat j+3\hat k \), \( \vec b=3\hat i-5\hat j+\hat k \) and \( \vec c \) be a vector such that \( \vec a\times \vec c=\vec c\times \vec b \) and \( (\vec a+\vec c)\cdot(\vec b+\vec c)=168 \). Then the maximum value of \( |\vec c|^2 \) is:
