
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
Consider a large equilateral triangle constructed using toothpicks to create rows of small equilateral triangles, where each row has one less triangle than the row directly below it. Determine the number of toothpicks required if the base of the large triangle has 1002 small equilateral triangles.

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