
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 $f(x)=(x-1)e^{x}- \frac {1}{3}ax^{3}- \frac {1}{2}x^{2}+1$ where $a\in\mathbb{R}$.  
$(1)$ When $a=0$, find the intervals of monotonicity for $f(x)$;  
$(2)$ If the inequality $f(x)\geqslant 0$ holds true for all $x$ in the interval $[0,+\infty)$, find the range of values for the real number $a$.

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