
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 $f(x)=ax\ln(x+1)+x+1$ $(x > -1,a\in\mathbb{R})$.
- $(1)$ If $a= \frac{1}{e}$, find the intervals of monotonicity for the function $f(x)$.
- $(2)$ When $x\geqslant 0$, the inequality $f(x)\leqslant e^{x}$ always holds, find the range of the real number $a$.

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