
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
Find a center of symmetry of the graph of the function $g(x)=(M+m)x+\sin \left[(M+m)x-1\right]$, given that the maximum and minimum values of the function $f(x)= \frac {2(x+1)^{2}+\sin x}{x^{2}+1}$ are $M$ and $m$ respectively.

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