For cogo (collect) and cogito (re-collect) have the same relation to each other as ago and agito, facio and factito.
It required all the rest of the day to re-collect our party and to repair damages.
Beaten and sullen, the god again retired to re-collect his strength.
When his household cares obliged the ministrant to leave her room, Nydia began to re-collect her thoughts.
The King lay for some moments silent, but evidently striving to re-collect his thoughts.