
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 $f(x)=\ln x-ax+1$ where $a\in \mathbb{R}$:
1. Discuss the monotonicity of the function $f(x)$.
2. If $a=-2$, determine whether there exists a real number $m (m\in \mathbb{N}^{*})$ such that $f(x)\leqslant m(x+1)$ always holds. If it exists, find the minimum value of the real number $m$; if it does not exist, provide a reason.

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