Laptop CPU / GPU overheating during Gaming

First, thank you for taking time to look at my issue. I am not tech savvy.

My laptop automatically shuts itself off after about 10 minutes of gaming, which it never had a problem running in the past. Because I was not able to turn on the laptop for a few minutes after it blacks out, and because it ONLY happens while gaming when the fans are running on max, I deduced that it was overheating.

Since then, I have done a few things. I installed CPUID HWMonitor to see how hot my laptop was getting. I opened my laptop and cleaned the fan, which did not seem dusty at all, and carefully cleaned and replaced the thermal paste on my CPU and under the heat sink. It definitely helped, and I was able to play games for about 2 hours before my laptop gave up again, after plugging it in to charge while still playing. I have never seen the temps the CPU and GPU got to before powering off, BUT at idle my CPU runs at about 65 degrees celcius and my GPU runs at 60. During gaming, my CPU gets around 80 degrees celcius, and my GPU is around 81-83, maxing at around 89. I have limited the power my CPU can have to 40% using the power management tool, and I have reduced the graphics of my game to the lowest setting. I also have an outside fan working on my laptop, although I am looking to buy a cooling pad as the next solution.

I don't know what to do. There is NOT a heat sink about my GPU, and THAT is what I think is overheating and causing the laptop to turn off. Any input would be so greatly appreciated as to what I can do because honestly a cooling pad is just a band-aid on the problem.

I don't know much about laptops, but apparently I have an HP Laptop 15, using an AMD Radeon R7, 8 GB of RAM in a 64-bit system with Windows 10...any help is so welcome. Thank you again.