
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 $f(x) = x \ln x + ax + b$ at the point $(1, f(1))$ with the tangent line $3x - y - 2 = 0$.
(1) Find the analytical expression for the function $f(x)$;
(2) If $k \in \mathbb{Z}$ and there exists $x > 0$ such that $k > \frac{f(x + 1)}{x}$, find the minimum value of $k$.

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