1 to explore

2 to probe

1 to search (a place)

2 to search (a database etc)

1 to retrieve (data)

2 to look up

3 retrieval

4 search

1 to act without taking time to think (idiom); to react instantly

2 to fire from the hip

1 nimble

1 to act without taking time to think (idiom); to react instantly

2 to fire from the hip

1 to mull over (idiom)

2 to think long and hard

1 lit. looking for a fine horse using only a picture (idiom)

2 fig. to do things along rigid, conventional lines

3 to try and find sth with the help of a clue

1 to rack one's brains (for apt wording etc) (idiom)

1 extortion and blackmail (idiom)