
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 a sequence $\{a_n\}$, for any $n \in \mathbb{N}^*$, it holds that $a_{n+2} = a_{n+1} - a_n$. If the sum of the first 63 terms of this sequence is 4000, and the sum of the first 125 terms is 1000, then the sum of the first 2011 terms is ____.

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