
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 that the function $f(x)$ is an even function on $(-\infty, +\infty)$, and for $x \geq 0$, it holds that $f(x+2) = -f(x)$, and when $x \in [0, 2)$, $f(x) = \log(x+1)$. Evaluate the value of $f(-2001) + f(2012)$.

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