
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 $f(x)=\log _{a}(x-a)+1$, where $(a > 0$ and $a\neq 1)$, it always passes through the fixed point $(3,1)$.
(I) Find the value of the real number $a$;
(II) Let the function $h(x)=a^{x}+1$, and the graph of the function $F(x)=[h(x)+2]^{2}$ is always above the graph of the function $G(x)=h(2x)+m+2$, find the range of values of the real number $m$.

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