
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 functions $f(x)=\frac{ax}{{e}^{x}}+\frac{{x}^{2}}{2}-x$ and $g\left(x\right)=\ln x$, where $e$ is the base of the natural logarithm.<br/>$(1)$ When $a=1$, find the extreme values of the function $f\left(x\right)$;<br/>$(2)$ Let $\max \{m,n\}$ represent the maximum of $m$ and $n$. Define the function $h\left(x\right)=\max \{f\left(x\right),g\left(x\right)\}$ for $x>0$. When $a\geqslant 0$, discuss the number of zeros of the function $h\left(x\right)$ on $\left(0,+\infty \right)$.

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