
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 $f(x) = \frac{a}{2}x^2 + (a + 1)x + 2\ln(x - 1)$.
(I) If the tangent line of the curve $y = f(x)$ at the point $(2, f(2))$ is parallel to the line $2x - y + 1 = 0$, find the equation of this tangent line;
(II) Discuss the monotonic intervals of the function $f(x)$.

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