
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
Let the function $f(x)=\log_a(1+x)+\log_a(3-x)$ where $x > 0, a \neq 1$, and $f(1)=2$.

(1) Find the value of $a$ and the domain of $f(x)$;

(2) Find the range of $f(x)$ on the interval $\left[0, \frac{3}{2}\right]$.

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