
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 $f(x)=ax^{2}+2x-\ln(x+1)$ (where $a$ is a constant),  
(1) When $a=-1$, find the intervals of monotonicity for the function $f(x)$;  
(2) Find the range of real numbers $a$ such that the inequality $f(x) \leqslant x$ holds true for all $x \in [0, +\infty)$.

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