
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 $f(x)= \frac {e^{x}-a}{x}$, $g(x)=a\ln x+a$.  
(1) When $a=1$, find the monotonic interval of $F(x)=f(x)-g(x)$;  
(2) If for $x > 1$, the graph of the function $y=f(x)$ is always above the graph of the function $y=g(x)$, find the range of the real number $a$.

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