Let $a,b,c,d$ be four distinct integers such that: $$\text{min}(a,b)=2$$$$\text{min}(b,c)=0$$$$\text{max}(a,c)=2$$$$\text{max}(c,d)=4$$ Here $\text{min}(a,b)$ and $\text{max}(a,b)$ denote respectively the minimum and the maximum of two numbers $a$ and $b$. Determine the fifth smallest possible value for $a+b+c+d$