Rule reminder
GERUND (same subject): avendo/essendo + past participle (prior action) or -ando/-endo (simultaneous). PARTICIPIO ASSOLUTO (different subject): past participle agreeing with its own noun/subject in gender and number. Both are formal alternatives to causal conjunctions. Choose based on whether the subjects are the same (gerund) or different (participio assoluto).
…__ (partire) in ritardo, non riuscirono a prendere il treno.