
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 $f(x)=(x^{2}-a+1)e^{x}$ $(a\in\mathbb{R})$ has two distinct extreme points $m$ and $n$ $(m < n)$, and $|m+n|+1\geqslant |mn|$.
(1) Find the range of the real number $a$;
(2) When $x\in[0,2]$, let the maximum value of the function $y=mf(x)$ be $g(m)$, find $g(m)$.

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