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

(1) Find the range of values for the real number $a$ if the inequality $f(x)\leqslant 2-|x-1|$ has a solution;

(2) When $a < 2$, the minimum value of the function $f(x)$ is $3$, find the value of the real number $a$.

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