
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 the interval $[-2014, 2014]$ and satisfying the conditions $f(x\_1+x\_2)=f(x\_1)+f(x\_2)-2012$ for any $x\_1$, $x\_2 \in [-2014, 2014]$ and $f(x) > 2012$ when $x > 0$, find the value of the sum of the maximum and minimum values of $f(x)$.

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