
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 $f(x)=(x-2)e^{x}- \frac {a}{2}x^{2}$, where $a\in\mathbb{R}$, and $e$ is the base of the natural logarithm  
(Ⅰ) Can the graph of the function $f(x)$ be tangent to the x-axis? If it can be tangent to the x-axis, find the value of the real number $a$; otherwise, please explain why;  
(Ⅱ) If the function $y=f(x)+2x$ is monotonically increasing on $\mathbb{R}$, find the maximum integer value that the real number $a$ can take.

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