
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 $f(x)=a\ln x-x+1$, where $a\in\mathbb{R}$.
$(1)$ Find the intervals of monotonicity for $f(x)$;
$(2)$ If $f(x)\leqslant 0$ holds for all $x\in(0,+\infty)$, find all possible values of the real number $a$.

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