
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 $f(x)=2a(\ln x-x)+x^{2}$ $(a>0)$ has two extreme points $x_{1}$ and $x_{2}$ $(x_{1} < x_{2})$, then the range of $f(x_{1})+f(x_{2})$ is ____.

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