
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 the function \( f(x)=x^{3}+\sin x \) (\( x \in \mathbf{R} \)), the function \( g(x) \) satisfies \( g(x)+g(2-x)=0 \) (\( x \in \mathbf{R} \)). If the function \( h(x)=f(x-1)-g(x) \) has exactly 2019 zeros, what is the sum of all these zeros?

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