Epicheirēō (ἐπιχειρέω) means to put one's hand to something — to attempt, undertake, or set about a task. From epi (upon) + cheir (hand). Luke uses it twice: in his prologue (many have "undertaken" to compile narratives) and in Acts (seven sons of Sceva "tried" to exorcise).
Luke's Gospel opens with epicheirēō: "Many have undertaken [epicheirēō] to draw up an account of the things that have been fulfilled among us" (1:1). Luke is situating his work in a stream of attempts — he is not the first, nor does he claim uniqueness, but he offers something more ordered and investigated. The Acts 19:13 use is darker: the Sceva sons "tried" (epicheirēō) to use Jesus' name as a formula without genuine relationship — and were overpowered by the demon. The contrast: Luke undertakes with the Holy Spirit's guidance (Luke 1:3 — "careful investigation"); the Sceva sons attempt with borrowed authority.
The "hand" (cheir) embedded in epicheirēō is intentional — it is not just thinking about something but putting hands to it. Luke's use in 1:1 is modest self-situating: he is one of many who have attempted the task, distinguished by carefulness and order. The Acts 19 use shows that epicheirēō in spiritual matters without genuine authority is dangerous presumption — you cannot use Jesus' name as an incantation if you don't know him.