put one’s mind to something —(also: set one’s mind to something) devote a lot of attention to a task:
- He put his mind to the problem of establishing a means of supporting those who had taken the pledge of abstinence.
turn one’s mind to something—begin to think seriously about smth.:
- I shook off my feelings of dread and turned my mind to finding a way out of there.
Cf.: turn someone’s mind to something—cause a person to think about smth.:
- I’ve been thinking about history … and your invitation turned my mind to the story of women in the West.