
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 $f(x)=2+\log_{3}x$, $x\in[1,9]$, and $g(x)=[f(x)]^{2}+f(x^{2})$,
(1) Find the domain of $g(x)$;
(2) Find the maximum value of $g(x)$ and the value of $x$ when $g(x)$ reaches its maximum.

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