
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 $f(x)=|2x−a|+a$.

(1) When $a=3$, find the solution set of the inequality $f(x)\leqslant 6$.

(2) Let $g(x)=|2x−1|$. When $x\in R$, it is always true that $f\left( x \right)+g\left( x \right)\geqslant 3$. Find the range of values for $a$.

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