
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 functions $f(x)=-x^{3}+ax-\frac{1}{4}, g(x)=e^{x}-e$, where $e$ is the base of the natural logarithm.

(Ⅰ) If the tangent line to the curve $y=f(x)$ at $(0,f(0))$ is perpendicular to the tangent line to the curve $y=g(x)$ at $(0,g(0))$, find the value of the real number $a$;

(Ⅱ) Let the function $h(x)=\begin{cases}f(x), & f(x)\geqslant g(x) \\ g(x), & f(x) < g(x)\end{cases}$, discuss the number of zeros of the function $h(x)$.

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