
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 $f(x) = (\log_{2}x - 2)(\log_{4}x - \frac{1}{2})$,
(1) Find the range of this function when $x \in [2,4]$.
(2) If $f(x) \geqslant m\log_{2}x$ for all $x \in [4,16]$, find the range of values for $m$.

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