
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 $f(x)=ax^{3}-x\ln x$, if for all $x_{1}, x_{2} \in (0, +\infty)$ and $x_{1} \neq x_{2}$, the inequality $(x_{1}^{2}-x_{2}^{2})(f(x_{1})-f(x_{2})) > 0$ always holds, then the range of values for the real number $a$ is \_\_\_\_\_\_.

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