
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 $f(x)=\ln x+x^2-ax$.

(I) If the function $f(x)$ is increasing in its domain, find the range of the real number $a$.

(II) Under the condition of (I), if $f(x)\leqslant \frac{1}{2}(3x^{2}+\frac{1}{x^{2}}-6x)$ always holds for $x\in(0,1]$, determine the range of $a$.

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