
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 $f(x)=\log _{a}(x-1)$ and $g(x)=\log _{a}(6-2x)$ $(a > 0$ and $a\neq 1)$.
(1) Find the domain of the function $φ(x)=f(x)+g(x)$;
(2) Determine the range of $x$ for the inequality $f(x)\leqslant g(x)$.

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