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Default Sumif function with a date range condition statement

I'm trying to sum the numbers in one column that fall within specified date
ranges listed in another column i.e. how many products were produced during a
given quarter throughout a fiscal year. The formula I've created looks
something like:

=SUMIF(L7:L226,"=AND(<9/30/2008,01/01/2009)",M7:M226)

or basically (SUMIF(dates column,date range condition, numbers column to sum))

I suspect that the problem lies within the formatting for the date range
condition, but I haven't been able to find the proper usage for using a date
range within a condition statement. Anyone out there know how to make this
work?
 
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