Have one mind (mian gnōmēn echousin). “One purpose” (gnōmē from ginōskō) as in Act 20:3; 1Co 1:10. The new powers are allies of the beast.
They give their power and authority unto the beast (tēn dunamin kai tēn exousian autōn tōi thēriōi didoasin). Present active indicative of didōmi. Just as the dragon gave both power and authority to the beast (Rev 13:2), so they are wholly at the service of the beast.