Pick out a couple of short stories and release them individually for free with a note at the end that others are available for a limited time at $2.99. For a long book, write a short standalone story featuring some of the characters and release that for free with a similar note at the end.
As others have said, a lot of people will download something if it is free and then forget all about it. But a very small minority of them will read it, especially if it is short, and they are the only people who will ever buy your full price book.
Another thing you might be able to do is team up with other short story writers working in the same genre and put out a bumper collection for free. That way you will all be sharing each other's readers, and you might all pick up a few new ones.
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