
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 $f(x) = a\ln x + bx$ ($a,b \in \mathbb{R}$), the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $x - 2y - 2 = 0$.

(Ⅰ) Find the expression for $f(x)$;

(Ⅱ) When $x > 1$, $f(x) + \frac{k}{x} < 0$ always holds, find the range of the real number $k$;

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