
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
Define a function f(x) on R that satisfies f(x+6) = f(x). When -3 ≤ x < -1, f(x) = -(x+2)^2; when -1 ≤ x < 3, f(x) = x. Evaluate the sum f(1) + f(2) + f(3) + ... + f(2012).

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