Lighting, Light Fixtures, Ceiling and Exhaust Fans - Recess lights not working

Hello,

One of the recess lights in our kitchen started flickering and in like 5-10 ten minutes all of the lights went off with a "Pop" sound. I have 4 lights in my kitchen and I replaced the "burnt" bulb with a new one. I also made sure that rests of the 3 bulbs are working.
I have 2 GFCI protected outlets in the kitchen and I noticed that they are not working, then I used the "reset" button in one of the outlets and all of the outlets are now working. But when I switch on the recess lights they are still not working. I checked my circuit breakers and they are all on.

So, even after replacing the "burnt" bulb and making sure that the other 3 bulbs are working, my recess lights are still not coming up in the kitchen. What could be the problem???
I appreciate any advice. I am not a great handy man but can do reasonable repairs.

Thanks in advance. :confused:

Time to do a bit of analysis. Shut off that breaker and check everything in your house for power. The idea it to make a complete list of everything on that circuit. Once you have that list (and please be thorough), post it here.

Also, tell us what, if any, electrical test instruments you own.

Also, tell us the wattage of these bulbs.