
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 $f(x)=\log_a(x+1)+\log_a(3-x)$ where $a > 0$ and $a \neq 1$, and $f(1)=2$,
(1) Find the value of $a$ and the domain of $f(x)$;
(2) If the inequality $f(x)\leqslant c$ always holds, determine the range of values for the real number $c$.

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