
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 $f(x)=x^{2}-2(a+1)x+2ax\ln x+2a+1$ where $a\in\mathbb{R}$.

$(1)$ When $a=-2$, find the monotonic intervals of $f(x)$ on $(0,2)$;

$(2)$ For all $x > 0$ and $x\neq 1$, if $\dfrac {2ax\ln x}{x-1} > 2a+1-x$ always holds, find the range of the real number $a$.

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