
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 $b_1, b_2, \dots, b_{2018}$ be a strictly increasing sequence of positive integers such that
\[ b_1 + b_2 + \cdots + b_{2018} = 2018^3.\]
Determine the remnants of $b_1^3 + b_2^3 +\cdots + b_{2018}^3$ and $b_1^4 + b_2^4 + \cdots + b_{2018}^4$ when divided by 5.
A) Cube remainder 3, Fourth Power remainder 3
B) Cube remainder 3, Fourth Power remainder 1
C) Cube remainder 1, Fourth Power remainder 3
D) Cube remainder 2, Fourth Power remainder 1

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