
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
Numbers that can be expressed as the sum of consecutive natural numbers starting from 1, such as $1=1$, $3=1+2$, $6=1+2+3$, $10=1+2+3+4$, $15=1+2+3+4+5$, $\cdots$, are called "triangular numbers." What is the first "triangular number" year in the 21st century (starting from the year 2000)?

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