
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 $f\left(x\right)=x-1+\frac{ax^{2}}{e^{x}}$ where $a\in \mathbb{R}$.  
$(1)$ When $a=1$, find the equation of the tangent line to $f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$.  
$(2)$ If $g\left(x\right)=e^{x-1}f\left(x-1\right)+x\left(1-\ln x\right)$ has two zeros for $x\in \left[1,+\infty \right)$, find the range of real numbers for $a$.

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