
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 $f(x)=\ln (1+x)$, $g(x)=xf′(x)$, where $f′(x)$ is the derivative of $f(x)$, and $x\geqslant 0$. Let $g_{1}(x)=g(x)$, $g_{n+1}(x)=g(g_{n}(x))$, $n∈N_{+}$, find the expression for $g_{n}(x)$.

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