
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 $a > 0$, suppose the function $f\left( x \right)=\frac{{{2016}^{x+1}}+2011}{{{2016}^{x}}+1}+{{x}^{3}}\left( x\in \left[ -a,a \right] \right)$ has a maximum value of $M$ and a minimum value of $N$. Find the value of $M+N$ (   ).

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