
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 $f(x)=x+ \frac{a}{e^{x}}$ (where $e$ is the natural base).
(1) When $a=e$, find the extreme value of the function $y=f(x)$;
(2) Does there exist a positive number $a$ such that $f(x) > a$ always holds true in the domain? If so, find such an $a$; if not, explain the reason.

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