
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 \( b_1, b_2, \ldots, b_{100} \) be a strictly increasing sequence of positive integers such that \( b_1 + b_2 + \cdots + b_{100} = 5050. \) Find the remainder when \( b_1^2 + b_2^2 + \cdots + b_{100}^2 \) is divided by 5.

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