When you use grep, and are looking for a phrase, there may be errors which dont contain the word ERROR so it is not fool proof in that way. Its a good skill to have though knowing how to grep your tail. That sounds a bit wrong eh haha.
Analyse log with a text editor
nano /home/coti/coti-node/logs/FullNode1.log
Example of what a working node looks like
If you somehow do not have a log from the above commands then your node may not even have produced a log yet. Something likely went wrong. The most common issues when users install the node is that they mix up their private key (64 characters long) with their secret key (8-15 characters long). Or, sometimes people use their mainnet keys instead of their testnet keys. Do not do this.
If all else fails run the uninstall and then install again and closely monitor the install script until you see the node behaving like the screenshot above or before that you may see a phrase COTI FULL NODE IS UP.