
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 $f(x)=\frac{1}{2}x^{2}+(1-x)e^{x}$ (where $e$ is the base of the natural logarithm), $g(x)=x-(1+a)\ln x-\frac{a}{x},a < 1$.

(1) Find the equation of the tangent line to the curve $f(x)$ at $x=1$;

(2) Discuss the minimum value of the function $g(x)$;

(3) If for any $x_{1} \in [-1,0]$, there always exists $x_{2} \in [e,3]$ such that $f(x_{1}) > g(x_{2})$ holds, find the range of the real number $a$.

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