Prove that for all positive real numbers $x, m, a, s$, $$6 + 6^{x+m} + 6^{x+m+a} + 6^{x+m+a+s} >\frac12(6^{x+1}) +\frac12(6^{m+1}) +\frac13(6^{a+1}) + 6^s$$