
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 \( f(x) = \log_a(1 + x) + \log_a(3 - x) \) with \( a > 0 \) and \( a \neq 1 \), and \( f(1) = 2 \):
1. Find the value of \( a \) and the domain of \( f(x) \).
2. Find the maximum value 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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