
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
Draw 63 lines on a coordinate plane: \( y = b, y = \sqrt{3} x + 2b, y = -\sqrt{3} x + 2b \), where \( b = -10, -9, -8, \cdots, 8, 9, 10 \). These lines divide the plane into several equilateral triangles. The number of equilateral triangles with side length \( \frac{2}{\sqrt{3}} \) is $\qquad$

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