
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 $f(x)= \frac {1}{2}x^{2}+2ax(x > 0)$, $g(x)=3a^{2}\ln x+b$, where $a > 0$.  
(I) If $a=e$ when the two curves $y=f(x)$, $y=g(x)$ have a common point, and the tangents at the common point are the same, find the value of $b$;  
(II) If $f(x)\geqslant g(x)-b$ holds for any $x\in(0,+\infty)$, find the range of the real number $a$.

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