
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
Given the expansion of \(\left(1+x+x^{2}\right)^{1000}\) as \(a_{0}+a_{1} x+a_{2} x^{2}+\cdots+a_{2000} x^{2000}\), find the value of \(a_{0}+a_{3}+a_{6}+\cdots +a_{1998}\).

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