My best advice is don't run aground. Period. In most navies around the world, or shipping companies, if a captain grounds his or her command, he/she is removed for cause. I sort of approach sailing the same way. Thus, I don't run aground. And I ensure that through situational awareness and precautions in approaching unknown waters. If you are tempted to enter waters of which you lack a confident picture for any reason, and you are concerned about grounding, go someplace else. Once you start arguing with yourself on high tide/low tide, good chart/bad chart, one anchor/two anchors, you're already screwed.
Not trying to pick a fight here, but come on - really?
Your advice is sound at the beginning -- endeavor to not run aground in the first place. I think we can all agree that that's the best course of action. After that it gets a little preachy and holier than thou. Perhaps you are blessed with sailing grounds that don't include skinny water, and if so then my hat's off to you.
Your advice of "If you are tempted to enter waters of which you lack a confident picture for any reason, and you are concerned about grounding, go someplace else
" would pretty well take much of the AICW off of the table for recreational sailors.
There's a huge difference between a multi-million dollar ocean going ship and your average recreational sailboat. First off, there's very little reason for these ocean going vessels to venture into relatively shallow waters that are not clearly marked shipping channels. Secondly, even a gentle grounding in one of those puppies is going to cost huge bucks to undo in terms of both floating them off and in returning them to full commission.
Recreational vessels OTOH spend most of their time outside of marked channels, often (at least here on the eastern half of the US) within a few vertical feet of the bottom. Every once in a while that narrow buffer disappears entirely, even with the best of intentions and attentiveness. The OP's question was "what next?"