
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 that the solution set of the inequality $|x-2|>3$ is the same as the solution set of the inequality $x^2-ax-b>0$ with respect to $x$.

(1) Find the values of the real numbers $a$ and $b$;  
(2) Find the maximum value of the function $f(x)=a\sqrt{x-3}+b\sqrt{44-x}$.

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