
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 that the sequence $\{b_n\}$ satisfies $b_{n+2} = |b_{n+1} - b_n|$, and $b_1 = 1$, $b_2 = a$ ($a \leq 1$, $a \neq 0$), when the period of the sequence $\{b_n\}$ is 3, calculate the sum of the first 2010 terms of the sequence $\{b_n\}$.

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