Concrete Leveling Question

[Brad P.]

Property we closed on last week has a raised concrete patio going into the front door. Concrete is in good condition, no cracks or spalling, but there is a sag in the middle which leads to standing water every time it rains.

What's the proper way to fix this? I've read a bunch of different things from "use a concrete leveling agent", "concrete leveling agents are crap", "overlay the existing concrete with a thin layer of new concrete", "NEVER overlay concrete on existing concrete", etc.

All we want to do is make the patio level to get rid of the standing water issue.