engage in, engage with

1. VERB

If you engage in an activity, you do it or are actively involved with it.[ FORMAL ]

• I have never engaged in the drug trade.
  

4. VERB

If you engage with something or with a group of people, you get involved with that thing or group and feel that you are connected with it or have real contact with it.

• She found it hard to engage with office life.
• engagement N-UNCOUNT : usu N with n     
  ... And she, too, suffers from a lack of critical engagement with the literary texts.

... Cobuild