
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 specific sequence, the first term is \(a_1 = 2022\) and the second term is \(a_2 = 2023\). For the remaining terms, the values are chosen so that \(a_n + a_{n+1} + a_{n+2} = 2n\) for all \(n \geq 1\). Determine \(a_{1000}\).

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