
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 $y = (\log_{2}x + 2) \cdot (2\log_{4}x - 4)$, where $1 \leqslant x \leqslant 8$.

(1) Let $t = \log_{2}x$, find the relationship between $y$ and $t$, and state the range of $t$.

(2) Find the range of the function.

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