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

(I) When $a=2$, find the solution set of the inequality $f\left( x \right)\geqslant 0$;

(II) Let the function $g\left( x \right)=f\left( x \right)+3\left| x-a \right|$, when $a=1$, the minimum value of function $g\left( x \right)$ is $t$, and $\frac{2}{m}+	he {1}{2n}=t(m > 0,n > 0)$, find the minimum value of $m+n$.

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