
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 $f(x)={e}^{x}+ax+\frac{1}{2}{x}^{2}$ where $a\in\mathbb{R}$.  
$(1)$ When $a=-1$, determine the monotonicity of $f(x)$.  
$(2)$ When $x\geqslant 0$, if $f(x)≥\frac{3}{2}{x}^{2}+3ax+{a}^{2}-2{e}^{x}$ always holds, find the range of real number $a$.

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