Yes, the first step is stop the leaks. There's no point repairing the ceiling tiles if the roof still leaks.
Get up and inspect the roof. If you can't do it, hire someone.
Use Dicor Self Leveling caulk on the horizontal surfaces. DO NOT use Silicone.
After you find and repair the leaks, the best thing would be cover the seams and areas that leaked with
Eternabond.
Or just use Eternabond to stop the leaks.
The important thing is, stop the leak before it does any more damage.
If you can't get to it right away, cover it with a tarp until you can make the repairs.
Keep us updated on your progress.