The idiom 'learn from past mistakes to avoid future ones' comes from 'Small Caution' in the Hymns of Zhou of the Book of Songs.
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毖 means 'to be careful'. In this short hymn the young King Cheng of Zhou, after his uncles rose in revolt, vows 予其惩,而毖后患 'I take warning, and guard against trouble to come'. Today 毖 is met almost only in 惩前毖后.