
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 $f(x)=\ln x+ \frac {1}{2}mx^{2}-2$ ($m\in\mathbb{R}$).  
$(1)$ The tangent line to the curve $y=f(x)$ at $(1,f(1))$ is perpendicular to the line $2x-y+3=0$, find the value of $m$;  
$(2)$ If the inequality $f(x)+2\leqslant mx^{2}+(m-1)x-1$ always holds for $x$, find the minimum integer value of $m$.

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