
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
(The full score for this question is 12 points)

Given the function $f(x) = \frac{ax+b}{x-2}$ ($a, b$ are constants), and the equation $f(x) - x + 12 = 0$ has two real roots, $x_1 = 3$, $x_2 = 4$.

(1) Find the expression for $f(x)$;

(2) Let $k > 1$, solve the inequality $f(x) < k$.

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