Given that x, y, and z are real numbers satisfying $x+y +z = 10$ and $x^2 +y^2 +z^2 = 50$, ﬁnd the maximum possible value of $(x + 2y + 3z)^2 + (y + 2z + 3x)^2 + (z + 2x + 3y)^2$.


Let's think step by step and output the final answer within \boxed{}.
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