Not a harmonic mean question

Algebra Level 4

Let x,y,z0x, y, z\geq 0 be reals such that x+y+z=1x+y+z=1. Find the maximum possible value of

x(x+y)2(y+z)3(x+z)4.x (x+y)^{2}(y+z)^{3}(x+z)^{4}.

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