
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
Ancient Greek mathematicians called the numbers $1$, $3$, $6$, $10$, $15$, $21\ldots$ triangular numbers. They have a certain regularity. If the first triangular number is denoted as $a_{1}$, the second triangular number as $a_{2}$, $\ldots$, and the $n$th triangular number as $a_{n}$, calculate $a_{1}+a_{2}$, $a_{2}+a_{3}$, $a_{3}+a_{4}$, $\ldots$, and hence deduce $a_{2020}+a_{2021}=$____.

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