
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 $f(x)=a\ln x+\frac{1-a}{2}x^{2}-x$.
(I) Discuss the monotonicity of $f(x)$ on $(0,+\infty)$ when $a < 1$;
(II) When $a=1$, for all $x > 0$, find the range of $b$ such that $bx+1\geqslant f(x)$ always holds.

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