
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 $x\in A$, and the range of the function is $[\sqrt{2},16]$. The function $g(x)=(\log_{2}x)^{2}-\log_{2}x^{2}$.
(1) Find the set $A$.
(2) Find the range of the function $y=g(x)$, where $x\in A$.

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