
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 $f(x)=xe^{x}-ax^{2}-x$, where $a\in R$.
(1) When $a=\frac{1}{2}$, find the monotonic intervals of the function $f(x)$;
(2) If $f(x)\geq xe^{x}+ax^{2}$ holds for all $x\geq 1$, find the range of values for the real number $a$.

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