4-Digit Numbers forming Longest Reverse-and-Add Sequence

Theorem
Let $m \in \Z_{>0}$ be a positive integer expressed in decimal notation.

Let $r \left({m}\right)$ be the reverse-and-add process on $m$.

Let $r$ be applied iteratively to $m$.

The $4$-digit integers $m$ which need the largest number of iterations before reaching a palindromic number are:
 * $6999, 7998, 8997, 9996$

all of which need $20$ iterations.

Proof
which is palindromic.

$7998$ and its reversal converge on the same sequence immediately: