
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 $f(x)= \frac {mx}{x^{2}+n}$ ($m, n\in R$) takes an extremum of 2 at $x=1$.

(1) Find the explicit expression for $f(x)$;

(2) When $x>0$, what is the maximum value of $f(x)$?

(3) Let $g(x)=x^{2}-2ax+a$, if for any $x_1\in R$, there always exists $x_2\in[-1, 0]$ such that $g(x_2) \leq f(x_1)$, find the range of the real number $a$.

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