The parametric curve $(x,y) = (\cos 2t, \cos^2 t),$ for real numbers $t,$ describes a line segment.  Find the length of this line segment.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The parametric curve $(x,y) = (\cos 2t, \cos^2 t),$ for real numbers $t,$ describes a line segment.  Find the length of this line segment.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{5}
The parametric curve $(x,y) = (\cos 2t, \cos^2 t),$ for real numbers $t,$ describes a line segment.  Find the length of this line segment.
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