The word that best fits here is I would say:
To show or make make something clear - Cambridge.
So your sentence could read:
They're demonstrating their intentions.
Here are examples of the usage in a wide variety of different contexts:
Here the reader seemed to be demonstrating intentions, expertise and a
level of public concern that was appropriate for someone of his age.
-- Analysing Political Speeches: Rhetoric, Discourse and Metaphor - Jonathan Charteris-Black.
... deictic elements depend for their success on contextual facts and
-- Linguistics Today: Facing a Greater Challenge - P. G. J. van Sterkenburg.
Finally, a section for the "Demonstration of Intentionality" is
developed by: (1) proposing the theoretical necessity for
-- Culturicide, Resistance, and Survival of the Lakota: (Sioux Nation) - James V. Fenelon.
...evidences critical and analytical understanding and that the pupils
are demonstrating intentions.
-- Art revision support document - Dormston Secondary School.