
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 $f(x)=(a+1)\ln x+ax^{2}+1$,

(I) Discuss the monotonicity of the function $f(x)$;

(II) Let $a < -1$. If for any $x_{1}, x_{2} \in (0, +\infty)$, $|f(x_{1})-f(x_{2})| \geqslant 4|x_{1}-x_{2}|$, find the range of $a$.

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