
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
Let the function $f(x)=ax^{2}-a-\ln x$, where $a\in\mathbb{R}$.

$(I)$ Discuss the monotonicity of $f(x)$;

$(II)$ Determine all possible values of $a$ such that $f(x) > \frac{1}{x}-e^{1-x}$ holds true in the interval $(1,+\infty)$.

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