Palindromic Date

The number $2002$ is palindromic because it is the same read from left to right as it is read from right to left.

There was one date in February of the year $2002$ where the eight digits are palindromic if the date is written in the British way (dd/mm/yyyy).

This is not palindromic written the American way (mm/dd/yyyy).

Is there any palindromic date written the American way that year?

Find the next occasions when palindromic dates occur written in each way and the number of days between them.