
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 $a+b=1$, for $\forall a, b \in (0, +\infty)$, $\frac {1}{a} + \frac {4}{b} \geq |2x-1| - |x+1|$ always holds,  
(Ⅰ) Find the minimum value of $\frac {1}{a} + \frac {4}{b}$;  
(Ⅱ) Find the range of $x$.

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