
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
What is the maximum number of triangles with vertices at the vertices of a regular 18-gon such that no two distinct sides of these triangles are parallel? The triangles can intersect and share vertices, but coinciding segments are considered parallel.

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