
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 \(a_1,a_2,\dots,a_{2023}\) be a strictly increasing sequence of positive integers such that
\[
a_1+a_2+\cdots+a_{2023}=2023^{2023}.
\]
What is the remainder when \(a_1^3+a_2^3+\cdots+a_{2023}^3\) is divided by \(6\)?
A) 0
B) 1
C) 2
D) 3
E) 5

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