You should be able to ask for a short-term lease -- that's what we did when our lease expired in December and we weren't moving out until June.
Also find out what happens when you break the lease - usually it's just a penalty like half a month's rent. Basically a cash grab.
I really hate it when they make you sign a lease every year. Here usually it's just the first year, then after that you rent month to month.
Try not to panic - you can just sign the lease and trust that you will find something.
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