A palindrome is a word, phrase, or positive integer that reads the same forwards and backwards. For example, "kayak" is a palindrome. The integers \(292\), \(11\), and \(6\,357\,536\) are also palindromes.
Determine the number of six-digit palindromic integers that are divisible by \(15\).
Note: An integer is divisible by \(3\) exactly when the sum of its digits is divisible by \(3\). For example, \(15\,972\) is divisible by \(3\) since \(1+5+9+7+2=24\) and \(24\) is divisible by \(3\). But \(14\,923\) is not divisible by \(3\) since \(1+4+9+2+3=19\) and \(19\) is not divisible by \(3\).