
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
For the function $f(x)$ defined on $[-2010, 2010]$ satisfying the conditions: for any $x_1, x_2 \in [-2010, 2010]$, we have $f(x_1+x_2) = f(x_1) + f(x_2) - 2009$, and when $x > 0$, $f(x) > 2009$, find the sum of the maximum and minimum values of $f(x)$.

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