
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
When Xiaoming was doing math problems, he found that $\sqrt{1-\frac{1}{2}}=\sqrt{\frac{1}{2}}$; $\sqrt{2-\frac{2}{5}}=2×\sqrt{\frac{2}{5}}$; $\sqrt{3-\frac{3}{{10}}}=3×\sqrt{\frac{3}{{10}}}$; $\sqrt{4-\frac{4}{{17}}}=4×\sqrt{\frac{4}{{17}}}$; $\ldots$; following this pattern, if $\sqrt{a-\frac{8}{b}}=a•\sqrt{\frac{8}{b}}(a$,$b$ are positive integers), then $a+b=\_\_\_\_\_\_$.

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