A parametric curve is defined by
\[(x,y) = (\sin^2 t, 2 \cos t),\]where $t$ ranges over all real numbers.

The same parametric curve can be defined by
\[(x,y) = (-s^2 - 2s, 2s + 2),\]where $s$ ranges over some interval $I.$  Find the interval $I.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A parametric curve is defined by
\[(x,y) = (\sin^2 t, 2 \cos t),\]where $t$ ranges over all real numbers.

The same parametric curve can be defined by
\[(x,y) = (-s^2 - 2s, 2s + 2),\]where $s$ ranges over some interval $I.$  Find the interval $I.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
[-2,0]
A parametric curve is defined by
\[(x,y) = (\sin^2 t, 2 \cos t),\]where $t$ ranges over all real numbers.

The same parametric curve can be defined by
\[(x,y) = (-s^2 - 2s, 2s + 2),\]where $s$ ranges over some interval $I.$  Find the interval $I.$
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