<|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
 0 < \(a_1 \le a_2 \le a_3 \le \ldots\) is an unbounded sequence of integers. Let \(b_n = m\) if \(a_m\) is the first member of the sequence to equal or exceed \(n\). Given that \(a_{19} = 85\), what is the maximum possible value of \(a_1 + a_2 + \ldots + a_{19} + b_1 + b_2 + \ldots + b_{85}\)? 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
1700
0 < \(a_1 \le a_2 \le a_3 \le \ldots\) is an unbounded sequence of integers. Let \(b_n = m\) if \(a_m\) is the first member of the sequence to equal or exceed \(n\). Given that \(a_{19} = 85\), what is the maximum possible value of \(a_1 + a_2 + \ldots + a_{19} + b_1 + b_2 + \ldots + b_{85}\)?
test