What is the range of the function $y=\log_2 (\sqrt{\cos x})$ for $-90^\circ< x < 90^\circ$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the range of the function $y=\log_2 (\sqrt{\cos x})$ for $-90^\circ< x < 90^\circ$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,0]
What is the range of the function $y=\log_2 (\sqrt{\cos x})$ for $-90^\circ< x < 90^\circ$?
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