
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 $f\left( x \right)=\left| 2x+1 \right|-\left| x-a \right|$.

(I) When $a=4$, find the solution set of the inequality $f\left( x \right) > 2$;

(II) If the solution set of the inequality $f\left( x \right)\geqslant \left| x-4 \right|$ contains $[ 2,3 ]$, find the range of values for the real number $a$.

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