<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 On the New Year’s table, four glasses are arranged in a row: the first and third contain orange juice, while the second and fourth are empty. While waiting for guests, Valya absentmindedly and randomly pours juice from one glass to another. Each time, she can take a full glass and pour all its contents into one of the two empty glasses.

Find the expected number of pourings required for the situation to be completely reversed: the first and third glasses empty, while the second and fourth glasses are full. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
6
On the New Year’s table, four glasses are arranged in a row: the first and third contain orange juice, while the second and fourth are empty. While waiting for guests, Valya absentmindedly and randomly pours juice from one glass to another. Each time, she can take a full glass and pour all its contents into one of the two empty glasses.

Find the expected number of pourings required for the situation to be completely reversed: the first and third glasses empty, while the second and fourth glasses are full.
test