
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 $f(x)=\frac{1}{2}{x}^{2}-ax+(a-1)\ln x$, where $a>1$, for any $x_{1}$, $x_{2}\in \left(0,+\infty \right)$ with $x_{1} > x_{2}$, it is known that $f(x_{1})-f(x_{2}) > x_{2}-x_{1}$. Determine the range of the real number $a$.

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