The 10-Digit Digital Clock

Consider a digital clock that shows both the date and time in the format HH:MM:SS Mo/Dy. For example, 14:15:56 09/03 is a possible display. Note that the clock is a 24-hour clock (times run from 00:00:00 to 23:59:59) and leading zeros are allowed.

If all ten digits 0-9 appear on the display, what is (a) the earliest, and (b) the latest date and time in the year this could happen?

Source: Original.

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