CAT 2025 Slot 2 — QA Question 2

If $\log _ { 64 } x ^ { 2 } + \log _ { 8 } \sqrt { y } + 3 \log _ { 512 } ( \sqrt { y } z ) = 4$, where $x , y$ and $z$ are positive real numbers, then the minimum possible value of $( x + y + z )$ is