
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
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?

Present the answer in LaTex format: \boxed{Your answer}
user