
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 $f(x)=a^{x}-e(x+1)\ln a-\frac{1}{a}(a>0$, and $a\neq 1)$, where $e$ is the base of the natural logarithm.
(1) When $a=e$, find the maximum value of the function $y=f(x)$ in the interval $x\in[0,2]$.
(2) If the function $f(x)$ has only one zero point, find the value of $a$.

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