
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 $\sqrt{2+ \frac{2}{3}}=2 \sqrt{ \frac{2}{3}}$, $\sqrt{3+ \frac{3}{8}}=3 \sqrt{ \frac{3}{8}}$, $\sqrt{4+ \frac{4}{15}}=4 \sqrt{ \frac{4}{15}}$, $\sqrt{5+ \frac{5}{24}}=5 \sqrt{ \frac{5}{24}},\cdots, \sqrt{10+ \frac{a}{b}}=10 \sqrt{ \frac{a}{b}}$, then by reasoning, we get $a+b=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$．

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