DK-GEORGMOHR 2022 Problem 2

A positive integer is a palindrome if it is written identically forwards and backwards. For example, $285582$ is a palindrome. A six digit number $ABCDEF$ , where $A, B, C, D, E, F$ are digits, is called cozy if $AB$ divides $CD$ and $CD$ divides $EF$ . For example, $164896$ is cozy. Determine all cozy palindromes.