
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 \( b_n = b_{n-1} - b_{n-2} + 1 \) for each \( n \geq 3 \). What is the sum of the first \( 2001 \) terms of this sequence if the sum of the first \( 1995 \) terms is \( 2001 \), and the sum of the first \( 2001 \) terms is \( 1995 \)?

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