
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 $f(x) = \lg \left(x+ \frac{a}{x}-2\right)$, where $x > 0$, $a > 0$.

(1) Find the domain of the function $f(x)$;

(2) If for any $x \in [2, +\infty)$, it always holds that $f(x) > 0$, determine the range of values for $a$.

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