
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
An even function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x+2) = -f(x)$ and is monotonic in the interval $[0,2]$. If there exists $x \in (0,2)$ such that $f(x) = 0$, then the sum of all roots of the equation $f(x) = 0$ in the interval $[2002, 2010]$ is ______.

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