Oh, everyone had posted an action already.
Day 2, at base.
Frederick spends some time mashing berries, and tries out various potentiallly magical phrases. Continuing through the day, he (6.1%, *1.4 for full day effort, 8.54% chance. 58.39. Nope. +1.9% next day)
RAM harvests wood. He spends a long time, and gathers 20 logs worth.
(1.1% chance to learn magic. 30.7, failed. +0.9 tomorow)
Schaudy souts with his butterfly. It can't find anything in a 4 map-tile radius around the base, but there seems to be something of intrest to the southwest. It was too late in the day to check it out fully.
(chance to infer something about the nature of magic: 1.5%. 64.4: another failure. +0.5%)
Research: Often can happen casually during other activities, although many typed of more advanced research would have massive penalties, it can also be actively researched. Each day has a percentage chance of success, and it goes up any time research is accomplished.
This is an emulation of the moment of inspiration that can occur in real life when working on a hard problem, and lucky/unlucky days, while alowing a persistant player to still succeed.
Varous factors may modify the probability or the probability gain for the next day, ranging from help from a more experienced person to reading a manual, or dedicated research attempts.
The numbers are whatever I feel like, based on effort spent researching, but trying to be at least somewhat fair.
This same process applies to more than just magic. In fact, magic will start off easier, as you can work on it even while attempting something else, but later progress much slower than a physical practice.