
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 $f(x)=ax-\frac{a}{x}-51nx$ and $g(x)=x^2-mx+4$,
(1) If $x=2$ is the extreme point of function $f(x)$, find the value of $a$;
(2) When $a=2$, if there exists $x_1\in(0,1)$ such that for all $x_2\in[1,2]$, $f(x_1)\geq g(x_2)$ holds true, find the range of values for the real number $m$.

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