I do not believe there is any common international system for this. Office actions do have dates and are usually coded in the data of patent offices by by type of action but do not carry serial numbers.
Individual cases and applications typically are given attorney docket numbers that end up on most all of the back-and-forth correspondence. They are made up by attorneys and agents for their own record keeping and have no official standing. And are optional.
The core identifiers that are official are application numbers. With a country prefix they will be unique world-wide. Each continuation or divisional will have a unique application number.