
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 $f(x) = (kx + b) \cdot e^x$, and the equation of the tangent line to the curve $y = f(x)$ at $x = 1$ is $y = e(x - 1)$.

(Ⅰ) Find the values of $k$ and $b$;  
(Ⅱ) Calculate $\int_{0}^{1} (x \cdot e^x) \, dx$.

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