
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
Let $y=f''(x)$ be the second derivative of $y=f'(x)$. A student found through exploration that the graph of any cubic function $f(x)=ax^{3}+bx^{2}+cx+d (a\neq 0)$ has a center of symmetry at $(x_{0}, f(x_{0}))$, where $x_{0}$ satisfies $f''(x_{0})=0$. Given the cubic function $f(x)=x^{3}+2x-1$, if $x_{1}+x_{2}=0$, then $f(x_{1})+f(x_{2})=$______; if $m$ and $n$ satisfy the equations $m^{3}-3m^{2}+5m-4=0$ and $n^{3}-3n^{2}+5n-2=0$, then $m+n=$______.

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