
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 30 equal parts. Lines drawn through the division points parallel to the sides of the triangle divide it into 900 small triangles. What is the maximum number of vertices of the division such that no two of them lie on the same drawn line or side?

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