
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
The function f(x) satisfies f(x+6)=f(x). When -3 ≤ x < -1, f(x) = -(x+2)^2, and when -1 ≤ x < 3, f(x) = x. Calculate the value of f(1) + f(2) + f(3) + … + f(2012).

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