
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 $f(x)=1-\frac{a{x^3}}{{e^x}}$ where $a\neq0$.<br/>$(1)$ Discuss the monotonicity of $f(x)$ on $(0,+\infty)$;<br/>$(2)$ If the inequality $2e^{x}f(x)\geq x^{3}\ln x+x^{2}+3x$ always holds, find the range of values for $a$.

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