
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
(1) Find the range of values of the real number $x$ such that the inequality $|2a+b|+|2a-b|\geqslant |a|(|2+x|+|2-x|)$ holds for any non-zero real numbers $a$ and $b$.
(2) Let the function $f(x)=(2\log _{4}x-\frac{1}{2})$. Find the range of values of the real number $m$ such that $f(x)\geqslant m\log_{4}x$ holds for any $x\in[4,16]$.

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