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While it is possible for the snake to go up the vent instead of down the drain you can't make that assumption when you only go out several feet. You need to go out as much as 25' to rule out that possibility. All you can do if the snake goes up the vent is to pull it back and try again. Eventually it will go down the drain. The best tool for this job is a power snake (see attached pic) which can be rented at a tool rental outlet. Hand powered auger type snakes can also work but are not as consistently effective.