The $2m$ numbers $$1\cdot 2, 2\cdot 3, 3\cdot 4,\hdots,2m(2m+1)$$are written on a blackboard, where $m\geq 2$ is an integer. A move consists of choosing three numbers $a, b, c$, erasing them from the board and writing the single number $$\frac{abc}{ab+bc+ca}$$After $m-1$ such moves, only two numbers will remain on the blackboard. Supposing one of these is $\tfrac{4}{3}$, show that the other is larger than $4$.