
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 $f(x) = \log_{2}(4x) \cdot \log_{2}(2x)$, where $\frac{1}{4} \leqslant x \leqslant 4$,
(1) If $t = \log_{2}x$, find the range of $t$;
(2) Find the maximum and minimum values of $f(x)$, and provide the corresponding $x$ values.

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