
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 $$f(x)=-alnx+x+ \frac {1-a}{x}$$
(I) Discuss the monotonicity of the function $f(x)$;
(II) Let $g(x)=e^x+mx^2-2e^2-3$, when $a=e^2+1$, there exists $x_2 \in [1, +\infty)$ such that $g(x_2) \leq f(x_1)$ for any $x_1 \in [1, +\infty)$, find the range of the real number $m$.

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