Arrange the steps of Joule’s reasoning in the order they establish internal energy.

1. Perform adiabatic work on a system by several different methods
2. Observe that the work needed between two given states is always the same
3. Conclude that adiabatic work is path-independent and defines a state function
4. Define heat as the difference between the energy change and the work for a non-adiabatic path

The measurement comes first: adiabatic work turned out path-independent no matter how it was delivered. Only that fact licenses defining $U$, and only once $U$ exists can heat be defined as the residual $Q = \Delta U - W$.