Prove that for $\forall$ $a,b,c\in [\frac{1}{3},3]$ the following inequality is true: $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\geq \frac{7}{5}$.
Problem
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: algebra, Inequality, inequalities