
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 $f(x)=a\ln x-bx$, where $a, b \in \mathbb{R}$.  
$(1)$ When $b=1$, discuss the monotonicity of the function $f(x)$.  
$(2)$ When $a=1$, $f(x) \leq -1$, and the inequality $f(x) \leq xe^{x}-(m+1)x-1$ always holds. Find the range of real number $m$.

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