
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
Each side of triangle \(ABC\) is divided into 8 equal segments. How many different triangles with vertices at the division points (points \(A, B, C\) cannot be the vertices of these triangles) exist such that none of their sides is parallel to any side of triangle \(ABC\)?

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