
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 $f(x)=x\ln (1+x)-a(x+1)$, where $a$ is a constant.

(Ⅰ) If the function $f(x)$ is monotonically increasing on the interval $[1,+\infty)$, find the range of values for $a$;

(Ⅱ) Determine the intervals of monotonicity for $g(x)=f'''(x)-\frac{ax}{x+1}$.

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