
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 $a, b \in (0, +\infty)$, and $2^a4^b=2$.  
(Ⅰ) Find the minimum value of $\frac {2}{a}+ \frac {1}{b}$.  
(Ⅱ) If there exist $a, b \in (0, +\infty)$, such that the inequality $|x-1|+|2x-3| \geq \frac {2}{a}+ \frac {1}{b}$ holds, find the range of the real number $x$.

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