
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
Let $a_1,a_2,\dots,a_{2021}$ be a strictly increasing sequence of positive integers such that \[a_1+a_2+\cdots+a_{2021}=2021^{2021}.\] Find the remainder when $a_1^3+a_2^3+\cdots+a_{2021}^3$ is divided by $6$.

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