
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 $f(x)=|2x+1|+|2x-3|$.

(1) Find the solution set for the inequality $f(x)\leqslant 6$.

(2) If for any $x\in\left[-\frac{1}{2},1\right]$, the inequality $f(x)\geqslant |2x+a|-4$ always holds, find the range of values for the real number $a$.

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