<|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
 A \(20 \times 19\) rectangle is plotted on the Cartesian plane with one corner at the origin and with sides parallel to the coordinate axes. How many unit squares do the two diagonals of this rectangle pass through? 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
74
A \(20 \times 19\) rectangle is plotted on the Cartesian plane with one corner at the origin and with sides parallel to the coordinate axes. How many unit squares do the two diagonals of this rectangle pass through?
test