
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 $f(x)=\ln x-mx^{2}+(1-2m)x+1$, where $m\in \mathbb{R}$.  
$(1)$ If $f(1)=-1$, find the value of $m$ and the extreme value of the function $f(x)$.  
$(2)$ Discuss the monotonicity of the function $f(x)$.  
$(3)$ If $f(x)\leqslant 0$ holds for all $x$ in the domain, find the smallest integer value of $m$.

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