
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 \((1 + x + x^2)^{100}\) as \(a_0 + a_1 x + a_2 x^2 + \cdots + a_{200} x^{200}\), find the value of \(a_0 + a_3 + a_6 + \cdots + a_{198}\).

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