
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 an equilateral triangle is divided into 5 equal parts. Then, lines are drawn through these division points parallel to the sides of the triangle. These lines and the sides of the triangle intersect at 21 points inside the triangle and on its perimeter. How many equilateral triangles have all three of their vertices at one of these intersection points?

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