Ordinarily, we do not want to conflate the Gospel accounts. We should not take the same scene from two different Gospels, merge the accounts, and try to make every detail fit into a single coherent historical event. Each Gospel was written fundamentally as a self-contained work with its own perspective.
Nonetheless, the Church received all four of them into the canon. So sometimes it does make sense to read across the Gospels, as long as they are showing us different moments.
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