The gerund ends in -ing and functions as a noun. The infinitive is the base form of a verb with to. A participle is a verb that ends in -ing (present participle) or -ed, -d, -t, -en, -n (past participle). Participles may function as adjectives, describing or modifying nouns. Therefore i'd say it would be participle
Their motivation allow them to survive. When Salva's uncle died he used his pain as a motivation while Nya to get her family water. I hope this helps!!