
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 $f(x)=(x-1)e^{x+1}+mx^{2}$, where $m$ is a constant and $m > - \frac {e}{2}$.  
(I) When $m=1$, find the equation of the tangent line to the curve $y=f(x)$ at point $P(-1,f(-1))$;  
(II) Discuss the monotonicity of the function $y=f(x)$;  
(III) When $0 < m \leqslant 6$, $g(x)=x^{3}- \frac {4}{x}-mx$, $x\in(0,2]$, if there exist $x_{1}\in\mathbb{R}$, $x_{2}\in(0,2]$ such that $f(x_{1})\leqslant g(x_{2})$ holds, find the range of the real number $m$.

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