
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
Elective 4-5: Special Topics on Inequalities  
Let the solution set of the inequality $|2x-1|<1$ be $M$, and let $a \in M$, $b \in M$.  
(Ⅰ) Compare the size of $ab+1$ and $a+b$;  
(Ⅱ) Let $\max A$ represent the maximum number in the set $A$, and let $h=\max\left\{ \frac{2}{\sqrt{a}}, \frac{a+b}{\sqrt{ab}}, \frac{2}{\sqrt{b}} \right\}$, find the range of $h$.

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