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It was a most uncomfortable ride downriver from the Elven King's great cavern, both for the dwarves stuffed inside the barrels as well as for you riding on top of an empty barrel that felt like riding on a very wide-bellied pony that keeps wanting to roll in the grass.
The barrels float merrily along the river, bouncing and rolling all the way. They are gathered together and tied into rafts by the elfs further downstream and sent along to the village of the Men at Long Lake, also known as Esgaroth upon the Long Lake, or "Lake-town" by those who dwell in these parts.
Wet and weary as you are, when the barrels arrive at Esgaroth, you (with your invisible ring on) jump ashore and assist the men in using long poles to pull the barrels onto shore. You pick out those that are riding lowest in the water as they are most likely to have the dwarves inside, and you drag them down the shore a bit so you can unload the dwarves without being discovered.
Unfortunately that part of the plan failed, and you are soon discovered by the men of Esgaroth. Turns out that a pole waving around seemingly on it's own got their attention.
Despite being discovered, the men welcome you to Lake-town and provide you with food and supplies for the rest of your journey, because Smaug has been terrorizing their town for many long years, and they are as anxious to get rid of the dragon as you are.
In addition to the supplies, they also provide you with a cache that they have cleverly hidden in the forest nearby, in hopes that it will help you on your journey. You will need to use the same tool that you used to retrieve the barrels (in the story above) to retrieve this cache. You will find this tool at the posted coordinates for stage 1.