<|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 Fedor's bookshelf, there are volumes of works by various authors. When a friend borrowed two volumes of Pushkin, Fedor noticed that he had fully read at least half of the remaining books. After the friend returned the two volumes of Pushkin and borrowed two volumes of Lermontov, Fedor realized that he had fully read less than one-third of the remaining volumes. What is the maximum number of volumes that could have been on Fedor's shelf? 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
12
On Fedor's bookshelf, there are volumes of works by various authors. When a friend borrowed two volumes of Pushkin, Fedor noticed that he had fully read at least half of the remaining books. After the friend returned the two volumes of Pushkin and borrowed two volumes of Lermontov, Fedor realized that he had fully read less than one-third of the remaining volumes. What is the maximum number of volumes that could have been on Fedor's shelf?
test