
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 $a\in\mathbb{R}$, and the function $f(x)=x^2-2ax+5$,

(1) If the inequality $f(x)>0$ always holds for any $x\in(0,+\infty)$, find the range of values of the real number $a$;

(2) If $a>1$, and both the domain and range of the function $f(x)$ are $[1,a]$, find the value of the real number $a$.

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