
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 $f(x)= \sqrt {\log _{2}x}+ \sqrt {16-4^{x-1}}$.
(1) Find the domain ($A$) of $f(x)$;
(2) If the zeros of the function $g(x)=x^{2}+ax+b$ are $-1.5$, find the range of $g(x)$ when $x \in A$.

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