
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 $f(x)=e^{x}(2x-1)$ and $g(x)=x-1$.  
$(1)$ Let $h(x)=\frac{f(x)}{g(x)}$, find the monotonic interval of the function $h(x)$;  
$(2)$ Let $\varphi(x)=2xe^{x}-e^{x}-ax+a$. If the function $\varphi(x)$ has two distinct zeros, find the range of the real number $a$.

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