the world > movement > rate of motion > move at specific rate [verb (intransitive)] > outstrip others or take the lead (3)
To guide a person in a required direction, by leading or accompanying him or her, or by giving instructions (also occasionally to show the road)…
To have a good start over one's pursuers; (figurative) to have made good progress in an activity.
Originally Horse Racing. to take up the running: to take the lead. Frequently figurative.