## Task 2 - 120712

Determine all three-digit natural numbers $z$ that each satisfy the following conditions simultaneously:

(1) The number $z$ is divisible by both 9 and 11.

(2) If the digit in the hundreds place of the number $z$ is swapped with the digit in the units place, a new three-digit number $z^{\prime}$ is obtained, which is $\frac{2}{9}$ of the number $z$.