
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 $f(x)=|2x-a|+|2x-1| (a \in \mathbb{R})$.

(I) When $a=-1$, find the solution set for $f(x) \leqslant 2$;

(II) If the solution set for $f(x) \leqslant |2x+1|$ contains the set $\left[\frac{1}{2}, 1\right]$, find the range of possible values for the real number $a$.

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