Baltic Way 2019

Let $m\ge 2$ be a positive integer. Consider the $2m$ numbers $$1\cdot 2,2\cdot 3,3\cdot 4,\dots ,2m(2m+1).$$ A move consists of choosing three numbers $a,b,c$, and replacing them with the single number $$\frac{abc}{ab+bc+ca}.$$ After $m-1$ such moves, only two numbers will remain. Supposing one of these is $\frac{4}{3}$, show that the other exceeds 4.