
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 $f(x)=x- \dfrac{1}{2}ax^{2}-\ln(1+x)$, where $a\in\mathbb{R}$:
1. If $x=2$ is the extremum point of $f(x)$, find the value of $a$;
2. Determine the intervals of monotonicity for $f(x)$;
3. If the maximum value of $f(x)$ on the interval $[0,+\infty)$ is $0$, find the range of $a$.

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