
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) = ln(x+1) - $\frac{ax^2 + x}{(x+1)^2}$, where 'a' is a constant.
(1) Discuss the monotonicity of f(x) when 1 < a ≤ 2.
(2) Find the maximum value of g(x) = xln(1 + $\frac{1}{x}$) + $\frac{1}{x}$ln(1 + x) when x > 0.

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