
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 $f(x)=a\ln x- \frac {1}{2}x^{2}+x$, $g(x)= \frac {1}{2}x^{2}-2x+1$.  
(I) When $a=2$, find the maximum and minimum values of $f(x)$ for $x\in[1,e^{2}]$ (Reference data: $e^{2}\approx7.4$);  
(II) If for all $x\in(0,+\infty)$, $f(x)+g(x)\leqslant 0$ always holds, find the value of the real number $a$.

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