Long Game Strategy conjecture for the Ordered Zeckendorf Game

Let $n$ be the initial number of copies of $F_1$ in the Ordered Zeckendorf game, and let the Long Game Strategy (LGS) be the priority-based strategy that performs switch moves, combines adjacent ones from the left, performs split moves from the right, and performs merge moves from the left. Long Game Strategy conjecture. The LGS has the longest game length. This conjecture would establish that the proposed strategy attains the maximal length $M(n)$ of the game, complementing the known upper bound on $M(n)$. Its status is unresolved in the supplied text.