
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 solution set of the inequality $|x-2|>1$ is equal to the solution set of the inequality $x^2-ax+b>0$ with respect to $x$.  
(Ⅰ) Find the values of the real numbers $a$ and $b$;  
(Ⅱ) Find the maximum value of the function $f(x)=a \sqrt {x-3}+b \sqrt {5-x}$, and the value of $x$ at which the maximum value is obtained.

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