
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 functions $f(x)=\ln x-e^{1-x}$ and $g(x)=a(x^{2}-1)-\frac{1}{x}$.
(1) Determine the number of zeros of the function $y=f(x)$ and explain the reasoning.
(2) Let $h(x)=g(x)-f(x)+\frac{e^{x}-ex}{xe^{x}}$. Discuss the monotonicity of $h(x)$.
(3) If $f(x) < g(x)$ holds true in $(1,+∞)$, find the range of values for the real number $a$.

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