
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
Consider a sequence $b_1, b_2, \ldots, b_{100}$ of strictly increasing positive integers such that the sum of the elements in this sequence is given by $b_1 + b_2 + \cdots + b_{100} = 1000$. Calculate the remainder when the sum of the cubes of the sequence elements, $b_1^3 + b_2^3 + \cdots + b_{100}^3$, is divided by $6$.
A) 0
B) 1
C) 2
D) 3
E) 4

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