
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 $f(x)=\log_{2}(x^{2}+2)$, vectors $\overrightarrow{a}=(m,1)$ and $\overrightarrow{b}=( \frac{1}{2}, \frac{m}{2})$, with $m > 0$, find the range of values for $m$ if $f( \overrightarrow{a}\cdot \overrightarrow{b})\geqslant f(| \overrightarrow{a}- \overrightarrow{b}|)$.

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