<|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
 All three-digit numbers from 100 to 999 are written consecutively without spaces. Kostya underlined $k$ consecutive digits in this sequence, and Andrey underlined another $k$ consecutive digits in this sequence. The $k$-digit numbers underlined by the boys are equal. What is the largest possible value of $k$ for which this could happen? 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
5
All three-digit numbers from 100 to 999 are written consecutively without spaces. Kostya underlined $k$ consecutive digits in this sequence, and Andrey underlined another $k$ consecutive digits in this sequence. The $k$-digit numbers underlined by the boys are equal. What is the largest possible value of $k$ for which this could happen?
test