
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
Let the function $f(x)=\ln (1+ax)+bx$, and $g(x)=f(x)-bx^{2}$.  
(Ⅰ) If $a=1$, $b=-1$, find the monotonic intervals of the function $f(x)$.  
(Ⅱ) If the tangent line to the curve $y=g(x)$ at the point $(1,\ln 3)$ is parallel to the line $11x-3y=0$.  
(i) Find the values of $a$ and $b$;  
(ii) Find the range of real numbers $k(k\leqslant 3)$ such that $g(x) > k(x^{2}-x)$ holds true for $x\in(0,+\infty)$.

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