This is the 12163rd most frequent Turkish word.
gülümsetti
"Made (someone) smile."
Here, 'gülümsetti' represents the causative form of 'to smile', implying 'made me smile'.
O, nazik bir jest yaparak beni gülümsetti.
He made me smile by performing a kind gesture.
In this sentence, 'gülümsetti' again functions as 'made [someone] smile', showing an external cause for the action of smiling.
Başarımı duyunca arkadaşımı gülümsetti.
When he heard about my achievement, he made my friend smile.
Here, 'gülümsetti' illustrates causing the speaker herself to smile due to the emotional impact of the author's story.