The difference between "adopt" and "use" when they refer to utilizing something

Both of "adopt" and "use" can represent utilize something. What is the difference? I feel "adopt" is more formal, but I am not sure of my feelings.

For instance, I am writing an academic paper. Could I use

We adopt the Jaccard index in our implementation.

Or shall I use

We use the Jaccard index in our implementation.

I cannot distinguish the difference between the above two sentences and would like to choose "adopt".

Thanks in advance!

To "adopt" does not merely mean to use. In order to adopt, you must start using it.

to take up and practice or use

Emphasis mine.

For instance, during the Neolithic, humans used both agriculture and fire, but they only adopted agriculture, since they had long used fire.