This is the 10423rd most frequent Catalan word.
presumir
To boast or show off.
Here, 'presumeix' means to boast or show off, typically in a prideful manner.
Ell sempre presumeix dels seus èxits.
He always boasts about his achievements.
In this sentence, 'presumir' conveys the act of being proud of oneself for an accomplishment.
Pots presumir d'haver fet un gran treball.
You can be proud of having done a great job.
Here, 'presumeix' is used in the sense of assuming or presuming something as a priori knowledge.