
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 $e = 2.71828\ldots$ 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 there is a tangent line $l_1$ at any point on the curve $h(x) = -f(x) - (a+1)x + 2a$, there always exists a tangent line $l_2$ at a point on the curve $g(x) = (x-1)a + 2\cos x$ such that $l_1 \perp l_2$, find the range of the real number $a$.

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