For my machine learning research project I want to fine-tune a large language model (LLM) for a specific reinforcement learning task. In this task an agent is a LLM augmented by execution environment (e.g. Python REPL). The agent interacts with a formal verifier. The goal of the agent is to solve an engineering task. I want to start with a pre-trained model satisfying the following conditions:
* The model can be efficiently fine-tuned using A100 Nvidia GPUs in under 100 GPU-hours;
* Trained on academic papers (e.g. arxiv) and code (e.g. Github);
* Publicly available.

Please, do the following:
1. What kind of model is best suited for my purpose? Please, don't repeat my conditions; instead give an advise on what else I should be looking at when picking a model.
2. Describe how to find such models, e.g. provide a reference to a website with a list of pre-trained LLM models or a good search query to find such a list.
3. Provide a few (3..5) options for me to use, listing advantages and disadvantages of each for my specific purpose.
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