1. Give "strong" LLM the task formulation and some labeled examples. Ask it to generate a prompt for the "weak" LLM.
2. Run "weak" LLM on the training set with generated prompt from 1, use replies as features for a smaller ML model (logreg, decision tree etc).
3. Pick examples from the training set that your small model is most wrong about and ask "strong" LLM to generate one more prompt (like in 1), except this time you are using the misclassified examples instead of random.
4. Run "weak" LLM on generated prompt from 3, add results as one more feature for your model.
5. Repeat 2 - 4 until your token budget for this task is exhausted or required score on cross validation set is reached.
I was thinking about creating an open source library that implements this, but I'm not sure if anyone really needs it. I suspect that people who need something like this already made their own implementation.