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Verb: keep up with
  1. Maintain the same pace or level as someone or something
    "He had to jog to keep up with his athletic friend"
     
  2. Stay informed about current events or developments
    "It's important to keep up with the news"
     
  3. Continue to be in contact with someone
    "I try to keep up with my old college friends through social medi"

Derived forms: keeps up with, kept up with, keeping up with