Do we need a Finite state machine framework to design a tracking system

My requirement is to build a tracking system .I have a domain model which passes through multiple sub systems before it reaches end of its life .My requirement is to identify by querying which sub systems it is currently in and what state it lies in

Object A moves from System 1 -->System 2-->System 3

If someone gives me Object A I should return its current state and all details by querying or calling System 3 .

It is basically a tracking system which can pass through N no of finite states and it will always be in a well defined state at any given point of time .

I was looking at Activity with Spring boot and spring state machine to have a state machine so that the state can be segregated from the actual business logic where I invoke different system to query its status .