
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 $f(x)=x^3+\sin x+1$, investigate the center of symmetry of the graph of the function $f(x)$, and using the definition of the center of symmetry, determine the value of $f(-2016)+f(-2015)+f(-2015)+f(-2014)+\ldots+f(2014)+f(2015)+f(2016)$.

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