
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 functions $f(x) = \log_a(1+x)$ and $g(x) = \log_a(1-x)$, where $a>0$ and $a \neq 1$.

(1) Let $a=2$, and the domain of function $f(x)$ is $[3, 63]$, find the maximum and minimum values of function $f(x)$.

(2) Find the range of $x$ for which $f(x) - g(x) > 0$.

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