If the circles \( x^{2}+y^{2}+6x+8y+16=0 \) and \( x^{2}+y^{2}+2(3-\sqrt{3})x+2(4-\sqrt{6})y = k+6\sqrt{3}+8\sqrt{6}, \, k>0 \), touch internally at the point \( P(\alpha,\beta) \), then \( (\alpha+\sqrt{3})^{2}+(\beta+\sqrt{6})^{2} \) is equal to ____________ .
