What can I do to lose weight quickly but safely?

You need a better agent. That weight with that height is underweight for you and could cause medical problems. You don't need to lose any more pounds. Do some stretches and pulls if you feel your skin isn't tight enough but that agent is setting you up for sickness and death if he thinks you are too fat. Your body will go into shutdown if you are underweight because it thinks you are starving it and it won't give up the pounds. You can slim better with exercise but don't cut calories for your own medical sake. Get a new agent if they think you are fat. That is far from fat. It's actually on the road to starvation. Why risk your life for anyone that thinks you need to be more slender than that. I watch modeling shows all the time and none of the models are that skinny. Most of them keep their weight at 105 to 110 which is still too skinny for some of them but a whole lot better than you are striving for. At least that weight won't kill them.