To what extent was the collapse of the ‘Abbasid dynasty caused by the Mongol invasion?

The question requires that candidates consider the merits or otherwise of the argument that the Mongol invasion of 1258 caused the collapse of the ‘Abbasid dynasty. Candidates may suggest that the Mongol chief Hülegü Khan killed the last ‘Abbasid sultan in the siege of Baghdad in 1258, and that this affirms the suggestion in the question. On the other hand, candidates may argue that the ‘Abbasid dynasty had long since collapsed in all but name. Candidates may argue that dynastic struggles for succession after Harun Al Rashid (d 809) greatly weakened the empire, as did territorial losses to rivals such as the Fatimids Turkish soldiers became the dominant military force in the empire and the Persian Shi‘a Buyids ruled the empire from 942, followed by the Seljuk Turks from 1055. Both groups maintained the ‘Abbasid Sultan but he had no political power.