
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 $f\left( x \right)=\left| \frac{1}{2}x \right|-\left| \frac{1}{2}x-m \right|$ with a maximum value of $4$.

(1) Find the value of the real number $m$;

(2) If $m > 0,0 < x < \frac{m}{2}$, find the minimum value of $\frac{2}{\left| x \right|}+\frac{2}{\left| x-2 \right|}$.

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