
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 $f(x)=\log_{2}(4x) \cdot \log_{2}(2x)$ with a domain of $[ \frac{1}{4},4]$.
(I) If $t=\log_{2}x$, find the range of $t$;
(II) Find the maximum and minimum values of $y=f(x)$, and find the corresponding $x$ values when the maximum and minimum values are obtained.

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