
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 $f(x)=e^{x}-ax-a$ where $a\in\mathbb{R}$, and $e=2.71828…$ is the base of the natural logarithm.

(Ⅰ) When $a=1$, find the minimum value of the function $f(x)$;

(Ⅱ) Discuss the monotonicity of $f(x)$;

(Ⅲ) Suppose that for any point on the curve $h(x)=-f(x)-(a+1)x+2a$, there exists a tangent line $l_{1}$ at this point, and there always exists a tangent line $l_{2}$ at some point on the curve $g(x)=(x-1)a+2\cos x$ such that $l_{1}⊥l_{2}$, find the range of the real number $a$.

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