
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 $f(x)=(a-1)\ln x+ax^{2}+1$.  
$(1)$ Discuss the monotonicity of the function $f(x)$.  
$(2)$ If for any $x_{1} > x_{2} > 0$, it always holds that $\dfrac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}\geqslant 2$, find the range of values for $a$.

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