I betray my origins. I grew up on the River Medway. That last 14 miles to the Nore. It is an stretch of water where a lot of really important things happened for over a 1000 years, that still affects us now.
It is rich in seafaring history. In my youth sailing barges without engines were still carrying cargoes around the south and East coast, up to the Humber.
In addition, our summer bolt hole was in Southwold Suffolk, a fishing port on the Suffolk coast and steeped in maritime history. I used to tell the time from the state of the tide from my window. So I had a lot of reason to grow up and be fluent in nautical terms, as are most who are raised in those part.
Anyhow, reef means pull, and usually hard. It refers to pulling on a sheet. Paradoxically it refers to a rope the pulls in a sail. So a command reef the mainsail, usually where I come from pronounced "mainsul". So on sailing barge the skipper would bark to his mate, "reef the minsul". "Aye, aye sir"! would come the reply. Other commands on a sailing barge would be '"reef the foresul! Reef the spritsul"!
So reef in those parts is synonymous with a hard pull.
This is a really interesting video, "Red Sails". These are my home waters, and I remember those barges from my youth.