The previous play that you've seen in a tournament should certainly influence your future play. You should constantly be observing the action and noting things like a player's calling. raising and shoving ranges. You should be observing player's tendency to bluff, or if they play a hand differently when they have from the way they play it when they don't. I've noticed such things as players that have a tendency to bet bigger with nothing, hoping to get a fold, and betting less with big hands to try to keep their opponent in the hand and calling.
The most basic decisions we are constantly making are whether to call, raise or fold. And each time those decisions should be based not only on our own cards, but also the play we've seen from our opponents. If I've seen a player constantly and repeatedly check/calling the flop and turn before suddenly shoving on the river, I'm more likely to suspect him of bluffing and therefore less likely to fold a solid hand to him when I see the same play from him in the future. It's also important to keep in mind that really good players are capable of switching up their play to keep you guessing.