
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 $f(x) = 4 - \log_{2}x$, $g(x) = \log_{2}x$.  
(1) When $x \in \left( \frac{1}{2}, 8 \right)$, find the range of the function $h(x) = f(x) \cdot g(x)$.  
(2) If for any $x \in [1, 8]$, the inequality $f(x^3) \cdot f(x^2) > kg(x)$ always holds, find the range of the real number $k$.

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