
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 $e$ is the base of the natural logarithm and $a \in \mathbb{R}$.

(I) Discuss the monotonicity of the function $y = f(x)$;

(II) The graph of the function $y = f(x)$ intersects the $x$-axis at two points $A(x_1, 0)$ and $B(x_2, 0)$, with $x_1 < x_2$. Point $C$ lies on the graph of $y = f(x)$, and $\Delta ABC$ is an isosceles right triangle. Let $\sqrt{\frac{x_2 - 1}{x_1 - 1}} = t$. Find the value of $at - (a + t)$.

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