to infinitive as an adjective clause expressing the intention/desire of the noun's agent

‘his action to observe the star’

(supposing that the phrase above is grammatically correct)

‘Action’ is just ‘action’. It itself doesn’t have any sensation of intention/desire. so we can conclude that this kind of a to-infinitive "specializes" in the meaning of ‘the intention/desire of the noun’s agent’. Then do Americans see this usage of to-infinitives as an adjective phrase expressing the meaning?
(Please stick to what Americans themselves would recognize them as by on their own, but not what the grammar says. Grammar comes after the recognization made by the speakers themselves. I want to make the analysis precisely and correctly.)