
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 chosen so that $b_n = b_{n-1} - b_{n-3}$ for each $n \ge 4.$ What is the sum of the first $2500$ terms of this sequence if the sum of the first $1800$ terms is $2300,$ and the sum of the first $2300$ terms is $1800$?

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