
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 $f(x)=(x+1)\ln x-ax+a$, where $a$ is a positive constant,  
(1) If $f(x)$ is monotonically increasing on $(0,+\infty)$, find the range of values for $a$.  
(2) If the inequality $(x-1)f(x)\geqslant 0$ always holds, find the range of values for $a$.

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