First impressions... Whether or not people should read a book by its cover, or the proverbial personality cover in this instance, the fact remains that most people do. So how you hit the floor running when you enter an organization will be very telling. This is a heads up to remember that in most cases, this is the norm. The only question might be is 100 days too long or do many organizations form an opinion much faster than that?
I would ask, what do you need to do to hit the floor running and stay running? Otherwise you'll be running to catch up, not lead. After a while it'll be more like hitting your head against the wall than evolving into any semblance of leadership. I'd also suggest learning as much as you can before walking through the front door. What is expected of you and by when? What do you need to know that you don't know in order to do your job in the best possible way? And if you don't know, then ask. Ask again. Ask someone else for their perspective. Don't forget to listen from a perspective of what you don't know. There's always more than one perspective. If others are holding back information, that says a lot about corporate culture and if the staff is collaborative or not. It'll also be a key determining factor as to how quickly you can get moving.
Balance those answers with your knowledge, innovative approach and energy. Integrate what others say to build a strong, cohesive team, not a dictatorship, and you'll have others on board to support you.
"Leaders don't force people to follow—they invite them on a journey." - Charles S. Lauer
Remember, in any context you have power with people, not by holding power over them. You'll all know within 3 months or less whether or not it's going to work. Cut that in half and you're ahead of the game.