In how many ways can 4 distinct beads be placed on a bracelet that has a knot in it?  (Beads cannot slide past the knot.  Two ways are considered the same if one is a reflection of the other, since we can flip the bracelet over.)
<|im_start|>system
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<|im_start|>user
In how many ways can 4 distinct beads be placed on a bracelet that has a knot in it?  (Beads cannot slide past the knot.  Two ways are considered the same if one is a reflection of the other, since we can flip the bracelet over.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
In how many ways can 4 distinct beads be placed on a bracelet that has a knot in it?  (Beads cannot slide past the knot.  Two ways are considered the same if one is a reflection of the other, since we can flip the bracelet over.)
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