
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 $b_1, b_2, \dots, b_{20}$ be a strictly increasing sequence of positive integers such that \[b_1+b_2+\cdots+b_{20}=420.\] What is the remainder when \(b_1^2 + b_2^2 + \cdots + b_{20}^2\) is divided by $5$?
A) 0
B) 1
C) 2
D) 3
E) 4

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