
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 complex number sequence $\left\{a_{n}\right\}$ satisfies: $a_{n+1}^{2}-a_{n} a_{n+1}+a_{n}^{2}=0 (n \geq 0)$, and $a_{n+1} \neq a_{n-1} (n \geq 1)$, with $a_{1}=1$, find the value of $\sum_{n=0}^{2006} a_{n}$.

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