
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
The sequence $\left\{a_{n}\right\}$ is: $1,1,2,1,1,2,3,1,1,2,1,1,2,3,4,\cdots$. The sequence is formed as follows: start with $a_{1}=1$ and copy this term to obtain $a_{2}=1$. Then add the number 2 as $a_{3}=2$. Next, copy all terms $1,1,2$ and place them as $a_{4}, a_{5}, a_{6}$, then add the number 3 as $a_{7}=3$, and so on. What is $a_{2021}$?

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