
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 $f(x)= \begin{cases} & x^{2}-x+3, x\leqslant 1, \\ & x+\frac{2}{x}, x > 1. \\ \end{cases}$

(I) Solve the inequality $f(x)\geqslant 3$;

(II) Suppose $a\in R$, and the inequality $f(x)\geqslant |\frac{x}{2}+a|$ holds for all $x\in R$. Find the range of $a$.

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