
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
Let  $n\geq3$  an integer. Mario draws  $20$  lines in the plane, such that there are not two parallel lines.
For each **equilateral triangle** formed by three of these lines, Mario receives three coins. 
For each **isosceles** and **non-equilateral** triangle (<u>at the same time</u>) formed by three of these lines, Mario receives a coin. How is the maximum number of coins that can Mario receive?

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