
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 $f(x)=|x-2|$.

(1) Solve the inequality: $f(x)+f(2x+1)\geqslant 6$;

(2) Given $a+b=1(a,b > 0)$, and for any $x\in R$, $f(x-m)-f(-x)\leqslant \frac{4}{a}+ \frac{1}{b}$ always holds, find the range of values for the real number $m$.

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