
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 that $P(m, n)$ is any point on the curve of function $f(x) = e^{x-1}$,
(Ⅰ) If the point $P$ is symmetrical to the point $Q(x, y)$ about the line $y = x - 1$, determine the relationship that the coordinates of point $Q$ must satisfy.
(Ⅱ) Given that the distance $d$ from point $M(x_0, y_0)$ to the line $l: Ax + By + C = 0$ is $d = \frac {|Ax_0 + By_0 + C|}{ \sqrt {A^2 + B^2}}$, when point $M$ lies on the curve of the function $y = h(x)$, the formula becomes $d = \frac {|Ax_0 + Bh(x_0) + C|}{ \sqrt {A^2 + B^2}}$. Refer to this formula to find the minimum value of the function $\omega(s, t) = |s - e^{x-1} - 1| + |t - \ln(t - 1)|$ where $s \in \mathbb{R}, t > 0$.

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