
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 functions $f(x)=x^{2}-ax$ and $g(x)=b+a\ln (x-1)$, there exists a real number $a(a\geqslant 1)$ such that the graph of $y=f(x)$ has no common points with the graph of $y=g(x)$. Determine the range of the real number $b$.

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