
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 $b_1, b_2, b_3, \ldots$ follows the rule $b_n = b_{n - 1} - b_{n - 2}$ for each $n \ge 3$. Find the sum of the first $2501$ terms of this sequence if the sum of the first $2007$ terms is $1522$ and the sum of the first $1522$ terms is $2007$.

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