
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 $f(x)=(x-1)e^{x}-\frac{a}{2}x^{2}$, where $a\in \mathbb{R}$.

(I) Can the graph of the function $f(x)$ be tangent to the $x$-axis? If so, find the real number $a$; if not, explain the reason.

(II) Find the largest integer $a$ such that for any $x_{1}\in \mathbb{R},x_{2}\in (0,+\infty )$, the inequality $f(x_{1}+x_{2})-f(x_{1}-x_{2}) > -2x_{2}$ always holds.

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