
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 quadratic inequality about $x$, ${x^{2}}+2mx+m+2\geqslant 0$, whose solution set is $R$.

(1) Find the range of the real number $m$.
(2) Find the minimum value of the function $f(m)=m+{\dfrac{3}{m+2}}$.
(3) Solve the quadratic inequality about $x$, ${{x}^{2}}+(m-3)x-3m > 0$.

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