
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 function $f(x)$ defined on $[-2016, 2016]$ and satisfying $f(a + b) = f(a) + f(b) - 2012$ for any $a, b \in [-2016, 2016]$, and $f(x) > 2012$ for $x > 0$, calculate the sum of the maximum and minimum values of $f(x)$.

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