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Here is one of the most useful facts about working with these models, and it falls straight out of the last slide. If you simply add "think step by step" to a hard question, the model gets noticeably more accurate. Researchers gave this a name: chain-of-thought.
It looks like a trick, but it is not. Remember, the model has no private place to do the work. Its only working memory is the text on the page, the context window we built in the last module. So when you ask it to spell out its steps, you are not giving it quiet time to think. You are giving it a place to think at all. Each step it writes goes onto the page, and the next word can attend back to those steps. The model is, in a real sense, leaving notes for itself to read a moment later.
The contrast matters. Forced to jump straight from a tricky question to a final answer, the model has to compress all the work into a single leap, and it often slips. Allowed to write the steps out, it builds a trail, and the answer rests on the trail instead of on a guess. Same model, same weights. The only difference is whether the reasoning got to happen out loud where the model could use it.
This is also why a model's longer, step-by-step answers tend to be more reliable than its snap ones. The reasoning is not hidden behind the words. It is the words, which means the more of it you let the model write, the more it has to stand on.