
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
A sequence of integers \( b_1, b_2, b_3, \ldots \) is defined such that \( b_n = b_{n-1} + b_{n-3} \) for each \( n \geq 4 \). Determine the sum of the first 2500 terms of this sequence if the sum of the first 1800 terms is 2000, and the sum of the first 2300 terms is 3000.

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