
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 $f(x)=ax^{3}+ \frac {2-3a}{2}x^{2}+bx$ (where $a,b$ are constants),

(1) If the tangent line to the graph of $y=f(x)$ at $x=2$ is $x-y+6=0$, find the expression for the function $f(x)$;

(2) Under the condition of (1), find the number of intersection points between the graph of $y=f(x)$ and the graph of $y=- \frac {1}{2}[f′(x)-9x-3]+m$;

(3) When $a=1$, for all $x\in(0,+\infty)$, $\ln x\leqslant f'(x)$ always holds, find the range of values for $b$.

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