CPU came out attached to heatsink
In some cases, when you remove the heat sink, the CPU might get out attached to the heat sink. DO NOT install it back into the socket like that, separate the CPU from the heat sink first.
CPU came out attached to the heat sink because thermal paste dried out and glued the processor.
Insert a flathead screwdriver between the CPU and the heat sink surface. Carefully rotate the screwdriver until the CPU separates from the heat sink.
Lift up the CPU and install it back into the socket on the motherboard. Now you can safely remove old thermal paste and apply a new layer of paste.