
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 $\mathbb{R}$ whose graph is symmetric with respect to the point $(1,1)$, $g(x)=(x-1)^{3}+1$. If the points of intersection between the graphs of $f(x)$ and $g(x)$ are given by $(x_{1},y_{1})$, $(x_{2},y_{2})$, …, $(x_{2018},y_{2018})$, then the value of $\sum\limits_{i=1}^{2018}(x_{i}+y_{i})$ is  
A) $8072$  
B) $6054$  
C) $4036$  
D) $2018$

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