You wouldn't be able to just register it, at least until it completely drops from the system. If you're lucky, renewing it would work.
Beyond that, by working with Yahoo, I basically mean show them that you're the legit owner, that you messed up, and that you'd really like to do what it takes to avoid losing the domain. Being polite and not letting any frustration show will definitely help out here.
It will require someone actually looking at it and helping you, though--not something that a script on a sign-up/renewal page will be able to do.
I'm not sure if they'll do it, or what proof they'd require from you, but it's worth trying.
There is one way you'd be screwed, and that would be if you used a fake name/address/email address to protect your privacy. I'm not suggesting you did, but some people do, rather than spend the $ for a privacy guard service. And this one of those times you want your personal info to be known and verifiable.
Hope that helps!
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