<|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
 In an acute triangle \( A B C \), altitudes \( A L \) and \( B M \) are drawn. Then, the line \( L M \) is extended to intersect the extension of side \( A B \).

What is the maximum number of pairs of similar triangles that can be counted in this diagram if no pair of congruent triangles is formed? 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
10
In an acute triangle \( A B C \), altitudes \( A L \) and \( B M \) are drawn. Then, the line \( L M \) is extended to intersect the extension of side \( A B \).

What is the maximum number of pairs of similar triangles that can be counted in this diagram if no pair of congruent triangles is formed?
test