I have a Pilot 2015, the passenger rear tire has a slow air leak. Obviously it triggers the TPMS message when it gets below a certain number. Today, I put air in the tire and discovered there is a nail in the groove of the tire which is the source of the leak. Obviously I don't know the size of the nail and how deep the puncture is in the tire.

How do I safely pull out the nail and patch the hole? Is there some kind of good patching kit to buy to clog the hole?