
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 $f(x)=x-a^{x}(a > 0$ and $a\neq 1)$.

(Ⅰ) When $a=e$, and $x$ takes all non-negative real numbers, if $f(x)\leqslant b-\frac{1}{2}{{x}^{2}}$, find the range of the real number $b$;

(Ⅱ) If the function $f(x)$ has a maximum value $g(a)$, find the minimum value of $g(a)$.

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