
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
In a new sequence, the first term is $b_1 = 3010$ and the second term is $b_2 = 3011$. Additionally, the terms are designed such that $b_n + b_{n+1} + b_{n+2} = n + 4$ for all $n \ge 1$. Determine $b_{1000}$.

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