
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 $f(x) = 2^x$ where the domain is $[0, 3]$, let $g(x) = f(2x) - f(x + 2)$.  
(1) Find the explicit formula for $g(x)$ and its domain.  
(2) If $x \in [0, 1]$, determine the maximum and minimum values of the function $g(x)$.

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