In my opinion, limbering up before activities is crucial for preparing your body and mind. For physical activities, the best routine include monotonous walking to increase circulation and mental strenght. I usually do this but not only before busy days but anyway as well.
Besides the physical aspects, mentally limbering up involves setting positive intentions, taking a few moments of mindfulness, or engaging in activities that stimulate focus. I think limbering up contributes to a more energized and focused approach to whatever lies ahead.