
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 $f(x)=ax-b(x+1)\ln(x+1)+1$, the equation of the tangent line at the point $(0,f(0))$ is $x-y+b=0$.  
$(I)$ Find the values of $a$ and $b$;  
$(II)$ If for $x \geqslant 0$, the inequality $f(x) \geqslant kx^{2}+x+1$ always holds, find the range of $k$.

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