
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 that the function $y=f(x)$ satisfies $f(x+y)=f(x)+f(y)$ for any $x,y \in \mathbb{R}$, and the function $g(x)=f(x)+\frac{x}{1+x^2}+1$, find $M+m$, where $M$ and $m$ are the maximum and minimum values of $g(x)$, respectively.

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