Isn’t that part of what the think blocks are for?
Yea, don’t inject them back into the context, but do log them for review of that train of thought… no?
Now recently some things have changed, and you can add the thinking part (you get that encrypted from the closed API labs). But the model needs to have been trained for this to work. And doing it this way you'll burn through tokens faster, as the thinking parts are usually rather long.