
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 $a > 0$, $b > 0$, let $A= \sqrt {a}+ \sqrt {b}$, $B=a+b$.
$(1)$ Find the maximum value of $\sqrt {2}A-B$;
$(2)$ If $ab=4$, is there any $a$, $b$ such that $A+B=6$? Explain your reasoning.

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