
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 $f(x) = (x^2 - ax + a + 1)e^x$,
(Ⅰ) Discuss the monotonicity of the function $f(x)$;
(Ⅱ) Suppose the function $f(x)$ has two extreme points, $x_1, x_2$ ($x_1 < x_2$), where $a > 0$. If $mx_1 - \frac {f(x_2)}{e^{x_1}} > 0$ always holds, find the range of real numbers $m$.

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