
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 $f(x)=kx-a^{x}$, where $k\in\mathbb{R}$, $a > 0$ and $a \neq 1$.
1. Discuss the monotonicity of $f(x)$ when $a=e$ (where $e=2.71\ldots$ is the base of the natural logarithm).
2. When $k=1$, if the function $f(x)$ has a maximum value denoted as $g(a)$, find the minimum value of $g(a)$.

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