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

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

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

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