
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 $f(x)=\ln x-ax^{2}$, $g(x)=f(x)+ax^{2}-x$.
(1) Find the extreme values of the function $f(x)$;
(2) Suppose $x_{1} > x_{2} > 0$, compare the size relationship between $\frac{x_{1}}{x_{1}^{2}+x_{2}^{2}}-\frac{g(x_{1})-g(x_{2})}{x_{1}-x_{2}}$ and $1$, and explain the reason.

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