The positive real numbers $a,b,c$ are such that $21ab+2bc+8ca\leq 12$. Find the smallest value of $\frac{1}{a}+\frac{2}{b}+\frac{3}{c}$.
Problem
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: algebra, inequalities