12.3.1.6 Algebraic

Problem: 4399 optionally different positive numbers \( v_{1}, v_{2}, \ldots, v_{4399} \) are written around the circle. For any 4 numbers \( h, k, z \) and \( p \), in a row in the indicated order clockwise, the inequality holds: \[ 1,6(h+k) \geq \frac{1}{z}+\frac{1}{p} \text {. } \] What is the smallest possible value of the arithmetic mean of these numbers? If the question of the problem allows several answers, then indicate all of them in the form of a set.