
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 $f(x)=e^{x}-ax+a$ ($a\in\mathbb{R}$), where $e$ is the base of the natural logarithm.
1. Discuss the monotonicity of the function $y=f(x)$.
2. The graph of the function $y=f(x)$ intersects the $x$-axis at points $A(x_{1},0)$ and $B(x_{2},0)$, where $x_{1} < x_{2}$. Point $C$ is on the graph of the function $y=f(x)$, and $\triangle ABC$ 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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