My best advice is just to do it. of course, that's not helpful, so let me suggest something more concrete: do an extremely easy case of a more interesting problem. While research problems can often seem quite daunting (and the ones worth doing take a while), try to chip off a piece of one you're pretty sure you can do, and do it. Older mathematicians may be able to help point you to some kind of appropriately non-difficult problem. It may not be worth publishing, but it may help get you rolling.
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