
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
Selected Exercise $(4-5)$: Inequality Lecture

Given the function $f(x)=|x-a|-|2x-1|$

(I) When $a=2$, find the solution set for $f(x)+3\geqslant 0$;

(II) When $x \in [1,3]$, find the range of values for $a$ such that $f(x) \leqslant 3$ always holds.

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