
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 $f(x)=\left| 2x-1 \right|+\left| x-a \right|, \ a\in R$.

(1) When $a=3$, solve the inequality $f(x)\leqslant 4$;

(2) If $f(x)=\left| x-1+a \right|$, find the range of $x$.

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