How to write correctness test for concurrent class?(that 2 actions is not executed in parallel )

I've got task to write my custom executor service.

I should work almost as usual but 2 tasks with same key(field of task) should not execute in parallel. I've wrote the code and I am sure that it should work correct.

But I need to write test. I haven't encountered the with test like this.

I could not google something useful about this.

Please, share your experience.