
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
If \( f(x) = \sum_{k=0}^{4034} a_k x^k \) is the expansion of \( \left(x^2 + x + 2\right)^{2017} \), calculate \( \sum_{k=0}^{1344} \left(2 a_{3k} - a_{3k+1} - a_{3k+2}\right) \).

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