A quartz crystal occupies the space in the first octant where 0 ≤ x ≤ 1, 0 ≤ z ≤ 1-x, and 0 ≤ y ≤ 3-x - z. The internal temperature of the crystal is given by the function T(x,y,z) = x in degrees celsius. What is the weighted average of the temperature over the entire crystal?

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