
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 so that $b_n = b_{n-1} - b_{n-2}$ for each $n \geq 3$. Determine the sum of the first $3001$ terms of this sequence if the sum of the first $2243$ terms is $2977$, and the sum of the first $2977$ terms is $2243$.

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