
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 $f(x)=|2x+1|+|2x-3|$.
- (I) Find the solution set of the inequality $f(x) \leqslant 6$;
- (II) If the solution set of the inequality $f(x) < |a-1|$ with respect to $x$ is non-empty, find the range of the real number $a$.

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