
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 $f(x)=\ln (1+x)-\frac{a{{x}^{2}}+x}{{{(1+x)}^{2}}}$.

(I) When $a=1$, find the equation of the tangent line to the function $f(x)$ at $x=e-1$.

(II) When $\frac{3}{2} < a\leqslant 1$, discuss the monotonicity of the function $f(x)$.

(III) If $x > 0$, find the maximum value of the function $g(x)={{(1+\\dfrac{1}{x})}^{x}}{{(1+x)}^{\\frac{1}{x}}}$.

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