
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 the interval $[-2016, 2016]$ that satisfies: for any $a, b \in [-2016, 2016]$, $f(a+b) = f(a) + f(b) - 2012$, and for $x > 0$, $f(x) > 2012$. If $M$ and $N$ are the maximum and minimum values of $f(x)$ respectively, then find the value of $M+N$.

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